Abstract For any finite group 𝐺 and a positive integer 𝑚, we define and study a Schur ring over the direct power G m G^{m} , which gives an algebraic interpretation of the partition of G m G^{m} obtained by the 𝑚-dimensional Weisfeiler–Leman algorithm. It is proved that this ring determines the group 𝐺 up to isomorphism if m ≥ 3 mgeq 3 , and approaches the Schur ring associated with the group Aut ( G ) operatorname{Aut}(G) acting on G m G^{m} naturally if 𝑚 increases. It turns out that the problem of finding this limit ring is polynomial-time equivalent to the group isomorphism problem.
{"title":"On multidimensional Schur rings of finite groups","authors":"Gang Chen, Qingchun Ren, Ilia N. Ponomarenko","doi":"10.1515/jgth-2023-0032","DOIUrl":"https://doi.org/10.1515/jgth-2023-0032","url":null,"abstract":"Abstract For any finite group 𝐺 and a positive integer 𝑚, we define and study a Schur ring over the direct power G m G^{m} , which gives an algebraic interpretation of the partition of G m G^{m} obtained by the 𝑚-dimensional Weisfeiler–Leman algorithm. It is proved that this ring determines the group 𝐺 up to isomorphism if m ≥ 3 mgeq 3 , and approaches the Schur ring associated with the group Aut ( G ) operatorname{Aut}(G) acting on G m G^{m} naturally if 𝑚 increases. It turns out that the problem of finding this limit ring is polynomial-time equivalent to the group isomorphism problem.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84448814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We say a group 𝐺 has property R ∞ R_{infty} if the number R ( φ ) R(varphi) of twisted conjugacy classes is infinite for every automorphism 𝜑 of 𝐺. For such groups, the R ∞ R_{infty} -nilpotency degree is the least integer 𝑐 such that G / γ c + 1 ( G ) G/gamma_{c+1}(G) has property R ∞ R_{infty} . In this work, we compute the R ∞ R_{infty} -nilpotency degree of all Generalized Solvable Baumslag–Solitar groups Γ n Gamma_{n} . Moreover, we compute the lower central series of Γ n Gamma_{n} , write the nilpotent quotients Γ n , c = Γ n / γ c + 1 ( Γ n ) Gamma_{n,c}=Gamma_{n}/gamma_{c+1}(Gamma_{n}) as semidirect products of finitely generated abelian groups and classify which invertible integer matrices can be extended to automorphisms of Γ n , c Gamma_{n,c} .
摘要:对于𝐺的每一个自同构域中，如果扭曲共轭类的个数R¹(φ) R(varphi)是无限的，则群𝐺具有R∞R＿ {infty}的性质。对于这样的群，R∞R＿ {infty} -幂零度是最小的整数𝑐，使得G/ γ c + 1¹(G) G/ gamma ＿ {c+1} (G)具有R∞R＿ {infty}的性质。在这项工作中，我们计算了所有广义可解Baumslag-Solitar群Γ n Gamma ＿ 的R∞R_ {infty} -幂零度。此外，我们计算了Γ n的下中心级数{}Gamma ＿ {n}，将幂零商Γ n, c = Γ n / Γ c + 1 (Γ n) Gamma ＿ {n,c} = Gamma ＿ {n} / gamma ＿ {c+1} (Gamma ＿ {n})作为有限生成的阿贝群的半直积，并对可逆整数矩阵可扩展为Γ n的自同态进行了分类。C Gamma ＿ {n,c}。
{"title":"The R ∞ R_{infty} property for nilpotent quotients of Generalized Solvable Baumslag–Solitar groups","authors":"Wagner C. Sgobbi, Da Silva, D. Vendrúscolo","doi":"10.1515/jgth-2022-0129","DOIUrl":"https://doi.org/10.1515/jgth-2022-0129","url":null,"abstract":"Abstract We say a group 𝐺 has property R ∞ R_{infty} if the number R ( φ ) R(varphi) of twisted conjugacy classes is infinite for every automorphism 𝜑 of 𝐺. For such groups, the R ∞ R_{infty} -nilpotency degree is the least integer 𝑐 such that G / γ c + 1 ( G ) G/gamma_{c+1}(G) has property R ∞ R_{infty} . In this work, we compute the R ∞ R_{infty} -nilpotency degree of all Generalized Solvable Baumslag–Solitar groups Γ n Gamma_{n} . Moreover, we compute the lower central series of Γ n Gamma_{n} , write the nilpotent quotients Γ n , c = Γ n / γ c + 1 ( Γ n ) Gamma_{n,c}=Gamma_{n}/gamma_{c+1}(Gamma_{n}) as semidirect products of finitely generated abelian groups and classify which invertible integer matrices can be extended to automorphisms of Γ n , c Gamma_{n,c} .","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88833587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We describe a method, based on curvature distribution techniques on van Kampen diagrams, for proving finitely presented groups hyperbolic. We apply our method and show that the generalised Fibonacci group F ( r , n ) F(r,n) is hyperbolic when r ≥ 3 rgeq 3 and n ≥ 6 r + 1 ngeq 6r+1 and determine which of the groups F ( 3 , n ) F(3,n) are hyperbolic.
{"title":"Curvature distribution and hyperbolicity","authors":"C. Chalk, M. Edjvet","doi":"10.1515/jgth-2022-0106","DOIUrl":"https://doi.org/10.1515/jgth-2022-0106","url":null,"abstract":"Abstract We describe a method, based on curvature distribution techniques on van Kampen diagrams, for proving finitely presented groups hyperbolic. We apply our method and show that the generalised Fibonacci group F ( r , n ) F(r,n) is hyperbolic when r ≥ 3 rgeq 3 and n ≥ 6 r + 1 ngeq 6r+1 and determine which of the groups F ( 3 , n ) F(3,n) are hyperbolic.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84051218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We prove that if L = F 4 2 ( 2 2 n + 1 ) ′ L={}^{2}F_{4}(2^{2n+1})^{prime} and 𝑥 is a nonidentity automorphism of 𝐿, then G = ⟨ L , x ⟩ G=langle L,xrangle has four elements conjugate to 𝑥 that generate 𝐺. This result is used to study the following conjecture about the 𝜋-radical of a finite group. Let 𝜋 be a proper subset of the set of all primes and let 𝑟 be the least prime not belonging to 𝜋. Set m = r m=r if r = 2 r=2 or 3 and m = r − 1 m=r-1 if r ⩾ 5 rgeqslant 5 . Supposedly, an element 𝑥 of a finite group 𝐺 is contained in the 𝜋-radical O π ( G ) operatorname{O}_{pi}(G) if and only if every 𝑚 conjugates of 𝑥 generate a 𝜋-subgroup. Based on the results of this and previous papers, the conjecture is confirmed for all finite groups whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, unitary simple group, or to one of the groups of type B 2 2 ( 2 2 n + 1 ) {}^{2}B_{2}(2^{2n+1}) , G 2 2 ( 3 2 n + 1 ) {}^{2}G_{2}(3^{2n+1}) , F 4 2 ( 2 2 n + 1 ) ′ {}^{2}F_{4}(2^{2n+1})^{prime} , G 2 ( q ) G_{2}(q) , or D 4 3 ( q ) {}^{3}D_{4}(q) .
{"title":"On generations by conjugate elements in almost simple groups with socle 2𝐹4(𝑞2)′","authors":"D. Revin, A. Zavarnitsine","doi":"10.1515/jgth-2022-0216","DOIUrl":"https://doi.org/10.1515/jgth-2022-0216","url":null,"abstract":"Abstract We prove that if L = F 4 2 ( 2 2 n + 1 ) ′ L={}^{2}F_{4}(2^{2n+1})^{prime} and 𝑥 is a nonidentity automorphism of 𝐿, then G = ⟨ L , x ⟩ G=langle L,xrangle has four elements conjugate to 𝑥 that generate 𝐺. This result is used to study the following conjecture about the 𝜋-radical of a finite group. Let 𝜋 be a proper subset of the set of all primes and let 𝑟 be the least prime not belonging to 𝜋. Set m = r m=r if r = 2 r=2 or 3 and m = r − 1 m=r-1 if r ⩾ 5 rgeqslant 5 . Supposedly, an element 𝑥 of a finite group 𝐺 is contained in the 𝜋-radical O π ( G ) operatorname{O}_{pi}(G) if and only if every 𝑚 conjugates of 𝑥 generate a 𝜋-subgroup. Based on the results of this and previous papers, the conjecture is confirmed for all finite groups whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, unitary simple group, or to one of the groups of type B 2 2 ( 2 2 n + 1 ) {}^{2}B_{2}(2^{2n+1}) , G 2 2 ( 3 2 n + 1 ) {}^{2}G_{2}(3^{2n+1}) , F 4 2 ( 2 2 n + 1 ) ′ {}^{2}F_{4}(2^{2n+1})^{prime} , G 2 ( q ) G_{2}(q) , or D 4 3 ( q ) {}^{3}D_{4}(q) .","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81422613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We prove that if 𝐺 is a connected semisimple algebraic group of rank 𝑟, and 𝐻 is a subgroup of 𝐺 that is contained in no proper parabolic subgroup, then we have | C G ( H ) | < c r | Z ( G ) | lvert C_{G}(H)rvert
摘要证明了如果𝐺是一个秩为𝑟的连通半简单代数群，且𝐻是𝐺的一个子群，且该子群不包含真抛物子群，则有| C G¹(H) | < C r¹| Z¹(G) | lvert c＿{g}(h)rvert
{"title":"A bound for the orders of centralizers of irreducible subgroups of algebraic groups","authors":"M. Liebeck","doi":"10.1515/jgth-2022-0111","DOIUrl":"https://doi.org/10.1515/jgth-2022-0111","url":null,"abstract":"Abstract We prove that if 𝐺 is a connected semisimple algebraic group of rank 𝑟, and 𝐻 is a subgroup of 𝐺 that is contained in no proper parabolic subgroup, then we have | C G ( H ) | < c r | Z ( G ) | lvert C_{G}(H)rvert<c^{r}lvert Z(G)rvert , where 𝑐 is an absolute constant ( c = 16 c=16 if all simple factors of 𝐺 are classical, and c ≤ 197 cleq 197 in general).","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90460034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A skew morphism of a finite group 𝐴 is a permutation 𝜑 of 𝐴 fixing the identity element and for which there is an integer-valued function 𝜋 on 𝐴 such that φ ( x y ) = φ ( x ) φ π ( x ) ( y ) varphi(xy)=varphi(x)varphi^{pi(x)}(y) for all x , y ∈ A x,yin A . In this paper, we restrict ourselves to the case when A = D n A=D_{n} , the dihedral group of order 2 n 2n . Wang et al. [Smooth skew morphisms of dihedral groups, Ars Math. Contemp. 16 (2019), 2, 527–547] determined all 𝜑 under the condition that π ( φ ( x ) ) ≡ π ( x ) ( mod | φ | ) ) pi(varphi(x))equivpi(x)pmod{lvertvarphirvert}) holds for every x ∈ D n xin D_{n} , and later Kovács and Kwon [Regular Cayley maps for dihedral groups, J. Combin. Theory Ser. B 148 (2021), 84–124] characterised those 𝜑 such that there exists an inverse-closed ⟨ φ ⟩ langlevarphirangle -orbit, which generates D n D_{n} . We show that these two types of skew morphisms comprise all skew morphisms of D n D_{n} . The result is used to classify the finite groups with a complementary factorisation into a dihedral and a core-free cyclic subgroup. As another application, a formula for the total number of skew morphisms of D p t D_{p^{t}} is also derived for any prime 𝑝.
摘要有限群的偏态射是一个固定单位元的变量的置换，对于这个置换，存在一个整数值函数，使得对于A x,y in A， φ∞(x) y = φ∞(x)∞(x)∞(x)∞(y) varphi (xy)= varphi (x) varphi{ ^ }{pi} (x)(y)。在本文中，我们限制了当A= dn A={D＿n}, 2次方n 2n的二面体群。Wang et al.[二面体群的光滑倾斜态射，数学学报。]当代16(2019)，2,527 - 547]在π (φ (x))≡π (x) (mod | φ |) pi (varphi (x)) equivpi (x) pmod{lvertvarphirvert})对每个x∈dn x in D＿n{成立的条件下确定了所有的变量，后来Kovács和Kwon[二面体群的正则Cayley映射，J. Combin]。理论SerB 148(2021)， 84-124]表征了那些变量，使得存在一个反封闭的⟨φ⟩}langlevarphirangle -轨道，它产生了dn {D＿n}。我们证明了这两种类型的倾斜态射包含了{dnd＿n}的所有倾斜态射。利用这一结果将具有互补分解的有限群划分为二面体和无核循环子群。作为另一个应用，对于{任意素数𝑝，也导出了{pdtd＿p ^}}t的偏态射总数的公式。
{"title":"A classification of skew morphisms of dihedral groups","authors":"Kan Hu, I. Kovács, Young Soo Kwon","doi":"10.1515/jgth-2022-0085","DOIUrl":"https://doi.org/10.1515/jgth-2022-0085","url":null,"abstract":"Abstract A skew morphism of a finite group 𝐴 is a permutation 𝜑 of 𝐴 fixing the identity element and for which there is an integer-valued function 𝜋 on 𝐴 such that φ ( x y ) = φ ( x ) φ π ( x ) ( y ) varphi(xy)=varphi(x)varphi^{pi(x)}(y) for all x , y ∈ A x,yin A . In this paper, we restrict ourselves to the case when A = D n A=D_{n} , the dihedral group of order 2 n 2n . Wang et al. [Smooth skew morphisms of dihedral groups, Ars Math. Contemp. 16 (2019), 2, 527–547] determined all 𝜑 under the condition that π ( φ ( x ) ) ≡ π ( x ) ( mod | φ | ) ) pi(varphi(x))equivpi(x)pmod{lvertvarphirvert}) holds for every x ∈ D n xin D_{n} , and later Kovács and Kwon [Regular Cayley maps for dihedral groups, J. Combin. Theory Ser. B 148 (2021), 84–124] characterised those 𝜑 such that there exists an inverse-closed ⟨ φ ⟩ langlevarphirangle -orbit, which generates D n D_{n} . We show that these two types of skew morphisms comprise all skew morphisms of D n D_{n} . The result is used to classify the finite groups with a complementary factorisation into a dihedral and a core-free cyclic subgroup. As another application, a formula for the total number of skew morphisms of D p t D_{p^{t}} is also derived for any prime 𝑝.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79876747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We will present an alternative approach to Zalesskiĭ’s theorem on diagonal embeddings of finite alternating groups.
摘要本文将给出zalesski’s关于有限交替群对角嵌入定理的一种替代方法。
{"title":"Diagonal embeddings of finite alternating groups","authors":"S. Thomas","doi":"10.1515/jgth-2022-0059","DOIUrl":"https://doi.org/10.1515/jgth-2022-0059","url":null,"abstract":"Abstract We will present an alternative approach to Zalesskiĭ’s theorem on diagonal embeddings of finite alternating groups.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80924387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we set η ( G ) eta(G) to be the number of conjugacy classes of maximal cyclic subgroups of a finite group 𝐺. We compute η ( G ) eta(G) for all metacyclic 𝑝-groups. We show that if 𝐺 is a metacyclic 𝑝-group of order p n p^{n} that is not dihedral, generalized quaternion, or semi-dihedral, then η ( G ) ≥ n - 2 eta(G)geq n-2 , and we determine when equality holds.
摘要:本文设η (G) eta (G)为有限群𝐺的极大循环子群的共轭类的个数。我们计算所有元环𝑝-groups的η∑(G) eta (G)。我们证明了如果𝐺是p n p^{n}阶的元环𝑝-group，它不是二面体、广义四元数或半二面体，则η∑(G)≥n-2 eta (G) geq n-2，并确定了等式在什么时候成立。
{"title":"Conjugacy classes of maximal cyclic subgroups of metacyclic 𝑝-groups","authors":"M. Bianchi, R. Camina, M. Lewis","doi":"10.1515/jgth-2022-0103","DOIUrl":"https://doi.org/10.1515/jgth-2022-0103","url":null,"abstract":"Abstract In this paper, we set η ( G ) eta(G) to be the number of conjugacy classes of maximal cyclic subgroups of a finite group 𝐺. We compute η ( G ) eta(G) for all metacyclic 𝑝-groups. We show that if 𝐺 is a metacyclic 𝑝-group of order p n p^{n} that is not dihedral, generalized quaternion, or semi-dihedral, then η ( G ) ≥ n - 2 eta(G)geq n-2 , and we determine when equality holds.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72541660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We prove that the order of a finite group 𝐺 with trivial solvable radical is bounded above in terms of acd ( G ) operatorname{acd}(G) , the average degree of the irreducible characters. It is not true that the index of the Fitting subgroup is bounded above in terms of acd ( G ) operatorname{acd}(G) , but we show that, in certain cases, it is bounded in terms of the degrees of the irreducible characters of 𝐺 that lie over a linear character of the Fitting subgroup. This leads us to propose a refined version of Gluck’s conjecture.
{"title":"The average character degree of finite groups and Gluck’s conjecture","authors":"Alexander Moret'o","doi":"10.1515/jgth-2022-0120","DOIUrl":"https://doi.org/10.1515/jgth-2022-0120","url":null,"abstract":"Abstract We prove that the order of a finite group 𝐺 with trivial solvable radical is bounded above in terms of acd ( G ) operatorname{acd}(G) , the average degree of the irreducible characters. It is not true that the index of the Fitting subgroup is bounded above in terms of acd ( G ) operatorname{acd}(G) , but we show that, in certain cases, it is bounded in terms of the degrees of the irreducible characters of 𝐺 that lie over a linear character of the Fitting subgroup. This leads us to propose a refined version of Gluck’s conjecture.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74759409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A finite group 𝐺 is normally monomial if all its irreducible characters are induced from linear characters of normal subgroups of 𝐺. In this paper, we study the largest irreducible character degree and the maximal abelian normal subgroup of normally monomial 𝑝-groups of maximal class in terms of 𝑝. In particular, we determine all possible irreducible character degree sets of normally monomial 5-groups of maximal class.
{"title":"Character degrees of normally monomial 𝑝-groups of maximal class","authors":"Dongfang Yang, Heng Lv","doi":"10.1515/jgth-2021-0212","DOIUrl":"https://doi.org/10.1515/jgth-2021-0212","url":null,"abstract":"Abstract A finite group 𝐺 is normally monomial if all its irreducible characters are induced from linear characters of normal subgroups of 𝐺. In this paper, we study the largest irreducible character degree and the maximal abelian normal subgroup of normally monomial 𝑝-groups of maximal class in terms of 𝑝. In particular, we determine all possible irreducible character degree sets of normally monomial 5-groups of maximal class.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91007576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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