{"title":"A characterization of finite $sigma$-soluble $Psigma T$-groups","authors":"C. Cao, Dein Wong, Chi Zhang","doi":"10.4171/rsmup/108","DOIUrl":"https://doi.org/10.4171/rsmup/108","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74110837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is H0 = PSL(2, q) with q = 2 f (f prime) such that cd(G) = cd(H), then there exists an abelian subgroup A of G such that G/A is isomorphic to H. In view of Huppert’s conjecture (2000), the main result of this paper gives rise to some examples that G is not necessarily a direct product of A and H, and consequently, we cannot extend this conjecture to almost simple groups. Mathematics Subject Classification (2010). Primary: 20C15; Secondary: 20D05
让G是一个有限群和cd (G)表示一组复杂的不可约特征度G在这篇文章中,我们证明,如果G是一个有限群和H几乎是一个简单的群是谁的脚柱H0 = PSL (2 q q = 2 f (f '), cd (G) = cd (H),然后有一个交换子群G, G / H的同构于佩尔猜想的看法(2000),本文的主要结果产生了一些例子,G未必是a股和H的直接产品,因此，我们不能把这个猜想推广到几乎简单的群上。数学学科分类(2010)。主:20 c15;二级:20 d05
{"title":"Huppert’s conjecture and almost simple groups","authors":"A. Daneshkhah","doi":"10.4171/rsmup/103","DOIUrl":"https://doi.org/10.4171/rsmup/103","url":null,"abstract":"Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is H0 = PSL(2, q) with q = 2 f (f prime) such that cd(G) = cd(H), then there exists an abelian subgroup A of G such that G/A is isomorphic to H. In view of Huppert’s conjecture (2000), the main result of this paper gives rise to some examples that G is not necessarily a direct product of A and H, and consequently, we cannot extend this conjecture to almost simple groups. Mathematics Subject Classification (2010). Primary: 20C15; Secondary: 20D05","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78747197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite groups with $H_{mathcal L}$-embedded subgroups","authors":"B. Hu, Jianhong Huang, A. Skiba","doi":"10.4171/rsmup/102","DOIUrl":"https://doi.org/10.4171/rsmup/102","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76188611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we prove that there are at most finitely many pairs of Fibonacci numbers (x, y) = (Fm, Fn) with the property that m ≤ n and the pair (m,n) 6∈ {(1, 2r− 1), (1, 2), (2, 2r+ 1), (2r+ 1, 2r+ 3) : r ≥ 1} such that (x, y, z) is a Markov triple for some integer z. Mathematics Subject Classification (2010). Primary: 11B39; Secondary: 11D61.
{"title":"Markov triples with two Fibonacci components","authors":"F. Luca","doi":"10.4171/rsmup/99","DOIUrl":"https://doi.org/10.4171/rsmup/99","url":null,"abstract":"In this paper, we prove that there are at most finitely many pairs of Fibonacci numbers (x, y) = (Fm, Fn) with the property that m ≤ n and the pair (m,n) 6∈ {(1, 2r− 1), (1, 2), (2, 2r+ 1), (2r+ 1, 2r+ 3) : r ≥ 1} such that (x, y, z) is a Markov triple for some integer z. Mathematics Subject Classification (2010). Primary: 11B39; Secondary: 11D61.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84224067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the following system (CA) consisting of one strongly nonlinear partial differential inclusion (PDI in short) with one linear PDE and one ODE, which describes a tumor invasion phenomenon with a haptotaxis effect and was originally proposed in [1]: (CA) ut −∇ · (du(v)∇β(v ;w)− u∇λ(v)) + β(v ;u) ∋ 0, vt = −avw, wt = dw∆w − bw + cu. This system has two interesting characteristics. One is that the diffusion coefficient du for the unknown function u in the partial differential inclusion depends on the function v, which is also unknown in this system. The other is that the diffusion flux ∇β(v ;u) of u also depends on v. Moreover, we are especially interested in the case that β(v ;u) is nonsmooth and degenerate in general under suitable assumptions. These facts make it difficult for us to treat this system mathematically. In order to overcome these mathematical difficulties, we apply the theory of evolution inclusions on the real Hilbert space V ∗, the dual space of V , with a quasi-variational structure for the inner products, which is established in [8], and show the existence of time global solutions to the initial-boundary value problem for this system. Mathematics Subject Classification (2010). Primary: 34G25; Secondary: 47J35, 49J40, 58E35.
{"title":"Quasi-variational structure approach to systems with degenerate diffusions","authors":"A. Ito","doi":"10.4171/rsmup/96","DOIUrl":"https://doi.org/10.4171/rsmup/96","url":null,"abstract":"We consider the following system (CA) consisting of one strongly nonlinear partial differential inclusion (PDI in short) with one linear PDE and one ODE, which describes a tumor invasion phenomenon with a haptotaxis effect and was originally proposed in [1]: (CA) ut −∇ · (du(v)∇β(v ;w)− u∇λ(v)) + β(v ;u) ∋ 0, vt = −avw, wt = dw∆w − bw + cu. This system has two interesting characteristics. One is that the diffusion coefficient du for the unknown function u in the partial differential inclusion depends on the function v, which is also unknown in this system. The other is that the diffusion flux ∇β(v ;u) of u also depends on v. Moreover, we are especially interested in the case that β(v ;u) is nonsmooth and degenerate in general under suitable assumptions. These facts make it difficult for us to treat this system mathematically. In order to overcome these mathematical difficulties, we apply the theory of evolution inclusions on the real Hilbert space V ∗, the dual space of V , with a quasi-variational structure for the inner products, which is established in [8], and show the existence of time global solutions to the initial-boundary value problem for this system. Mathematics Subject Classification (2010). Primary: 34G25; Secondary: 47J35, 49J40, 58E35.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"110 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75975265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given a torsor P under a principally polarised abelian scheme J , projective over a noetherian base, we use the Picard scheme of P to write down an explicit extension of Z by J giving the class of P . As an application we give a version of Bhatt’s period-index result valid over an arbitrary noetherian base.
{"title":"Torsors under abelian schemes via Picard schemes","authors":"R. Lodh","doi":"10.4171/rsmup/91","DOIUrl":"https://doi.org/10.4171/rsmup/91","url":null,"abstract":"Given a torsor P under a principally polarised abelian scheme J , projective over a noetherian base, we use the Picard scheme of P to write down an explicit extension of Z by J giving the class of P . As an application we give a version of Bhatt’s period-index result valid over an arbitrary noetherian base.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77783140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a differential system x d dxY = GY , where G is a m × m matrix whose coefficients are power series which converge and are bounded on the open unit disc D(0, 1−). Assume that G(0) is a diagonal matrix with p-adic integer coefficients. Then there exists a solution matrix of the form Y = F exp(G(0) log x) at x = 0 if all exponent differences are p-adically non-Liouville numbers. We give an example where F is analytic on the p-adic open unit disc and has log-growth greater than m. Under some conditions, we prove that if a solution matrix at a generic point has log-growth δ, then F has log-growth δ. Mathematics Subject Classification (2010). Primary: 12H25.
我们考虑一个微分系统x d dxY = GY，其中G是一个m × m矩阵，其系数是幂级数，幂级数收敛并在开单位圆盘d(0,1−)上有界。假设G(0)是一个具有p进整数系数的对角矩阵。如果所有指数差都是p非刘维尔数，则存在一个形式为Y = F exp(G(0) log x)在x = 0处的解矩阵。我们给出了F在p进开单位圆盘上解析且对数增长大于m的一个例子。在某些条件下，我们证明了如果解矩阵在一般点上具有对数增长δ，则F具有对数增长δ。数学学科分类(2010)。主:12 h25。
{"title":"On log-growth of solutions of $p$-adic differential equations with $p$-adic exponents","authors":"Takahiro Nakagawa","doi":"10.4171/rsmup/95","DOIUrl":"https://doi.org/10.4171/rsmup/95","url":null,"abstract":"We consider a differential system x d dxY = GY , where G is a m × m matrix whose coefficients are power series which converge and are bounded on the open unit disc D(0, 1−). Assume that G(0) is a diagonal matrix with p-adic integer coefficients. Then there exists a solution matrix of the form Y = F exp(G(0) log x) at x = 0 if all exponent differences are p-adically non-Liouville numbers. We give an example where F is analytic on the p-adic open unit disc and has log-growth greater than m. Under some conditions, we prove that if a solution matrix at a generic point has log-growth δ, then F has log-growth δ. Mathematics Subject Classification (2010). Primary: 12H25.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78490544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the nonexistence of minimizers for the energy containing a nonlocal perimeter with a general kernel K, a Riesz potential, and a background potential in R with N ≥ 2 under the volume constraint. We show that the energy has no minimizer for a sufficiently large volume under suitable assumptions on K. The proof is based on the partition of a minimizer and the comparison of the sum of the energy for each part with the energy for the original configuration. Mathematics Subject Classification (2010). 49J40, 49Q10, 49Q20, 28A75.
{"title":"Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential","authors":"F. Onoue","doi":"10.4171/rsmup/93","DOIUrl":"https://doi.org/10.4171/rsmup/93","url":null,"abstract":"We consider the nonexistence of minimizers for the energy containing a nonlocal perimeter with a general kernel K, a Riesz potential, and a background potential in R with N ≥ 2 under the volume constraint. We show that the energy has no minimizer for a sufficiently large volume under suitable assumptions on K. The proof is based on the partition of a minimizer and the comparison of the sum of the energy for each part with the energy for the original configuration. Mathematics Subject Classification (2010). 49J40, 49Q10, 49Q20, 28A75.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73643029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we give a proof via the contraction mapping principle of a Bloch-type theorem for (normalised) heat Bochner-Takahashi K-mappings, that is, mappings that are solutions to the heat equation, and which also satisfy a weak form of K-quasiregularity. We also provide estimates from below for the radius of the univalent balls covered by this family of functions.
本文利用压缩映射原理给出了(归一化)热Bochner-Takahashi k -映射的bloch型定理证明，即热方程的解的映射，也满足k -拟正则性的弱形式。我们还从下面给出了这组函数所覆盖的单价球的半径的估计。
{"title":"Bloch’s theorem for heat mappings","authors":"J. Cortissoz","doi":"10.4171/rsmup/92","DOIUrl":"https://doi.org/10.4171/rsmup/92","url":null,"abstract":"In this paper we give a proof via the contraction mapping principle of a Bloch-type theorem for (normalised) heat Bochner-Takahashi K-mappings, that is, mappings that are solutions to the heat equation, and which also satisfy a weak form of K-quasiregularity. We also provide estimates from below for the radius of the univalent balls covered by this family of functions.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77535777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A pseudovariety of semigroups is join irreducible if whenever it is contained in the complete join of some pseudovarieties, then it is contained in one of the pseudovarieties. A finite semigroup is join irreducible if it generates a join irreducible pseudovariety. New finite J -trivial semigroups Cn (n ≥ 2) are exhibited with the property that while each Cn is not join irreducible, the monoid C I n is join irreducible. The monoids Cn are the first examples of join irreducible J -trivial semigroups that generate pseudovarieties that are not self-dual. Several sufficient conditions are also established under which a finite semigroup is not join irreducible. Based on these results, join irreducible pseudovarieties generated by a J -trivial semigroup of order up to six are completely described. It turns out that besides known examples and those generated by C2 and its dual monoid, there are no further examples. Mathematics Subject Classification (2010). 20M07, 08B15.
{"title":"On join irreducible $J$-trivial semigroups","authors":"Edmond W. H. Lee, J. Rhodes, B. Steinberg","doi":"10.4171/rsmup/90","DOIUrl":"https://doi.org/10.4171/rsmup/90","url":null,"abstract":"A pseudovariety of semigroups is join irreducible if whenever it is contained in the complete join of some pseudovarieties, then it is contained in one of the pseudovarieties. A finite semigroup is join irreducible if it generates a join irreducible pseudovariety. New finite J -trivial semigroups Cn (n ≥ 2) are exhibited with the property that while each Cn is not join irreducible, the monoid C I n is join irreducible. The monoids Cn are the first examples of join irreducible J -trivial semigroups that generate pseudovarieties that are not self-dual. Several sufficient conditions are also established under which a finite semigroup is not join irreducible. Based on these results, join irreducible pseudovarieties generated by a J -trivial semigroup of order up to six are completely described. It turns out that besides known examples and those generated by C2 and its dual monoid, there are no further examples. Mathematics Subject Classification (2010). 20M07, 08B15.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75071740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：