Let G be a finite group. A subgroup L of G is said to be weakly-supplemented in G if there exists a proper subgroup M of G such that G = LM . The key of this paper is to determine the supersolvability and p -nilpotency of finite groups under assumption that some primary subgroups are weakly-supplemented.
{"title":"The influence of weakly-supplemented subgroups on the structure of finite groups","authors":"Yuxuan Zhang","doi":"10.12988/ija.2022.91729","DOIUrl":"https://doi.org/10.12988/ija.2022.91729","url":null,"abstract":"Let G be a finite group. A subgroup L of G is said to be weakly-supplemented in G if there exists a proper subgroup M of G such that G = LM . The key of this paper is to determine the supersolvability and p -nilpotency of finite groups under assumption that some primary subgroups are weakly-supplemented.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"19 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82878256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.1142/S0218196722500059
A. Price
{"title":"A Cayley graph for F2 × F2 which is not minimally almost convex","authors":"A. Price","doi":"10.1142/S0218196722500059","DOIUrl":"https://doi.org/10.1142/S0218196722500059","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"32 1","pages":"115-126"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63937097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Geraldo de Assis Junior, Karina Kfouri Sartori, Fernanda Goncalves de Paula
In this note we obtain necessary and sufficient conditions for that symmetric polynomial degree m let an polynomial identity for the algebras M n ( E ) and M a,b ( E ) when char K = p > 2.
本文给出了对称多项式次m对代数m n (E)和m a,b (E)在char K = p > 2时多项式恒等式的充分必要条件。
{"title":"The symmetric identity on Mn(E) and Ma,b(E)","authors":"Geraldo de Assis Junior, Karina Kfouri Sartori, Fernanda Goncalves de Paula","doi":"10.12988/ija.2022.91728","DOIUrl":"https://doi.org/10.12988/ija.2022.91728","url":null,"abstract":"In this note we obtain necessary and sufficient conditions for that symmetric polynomial degree m let an polynomial identity for the algebras M n ( E ) and M a,b ( E ) when char K = p > 2.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"494 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76704630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study characterizations of s-Σ-quasi-projective modules and properties of special star modules (tilting modules and Σ-quasi-projective self-generators) and characterize Σ-self-static star modules in terms of equivalences.
{"title":"Star modules and equivalences","authors":"Yong-lin Zhu","doi":"10.12988/ija.2022.91721","DOIUrl":"https://doi.org/10.12988/ija.2022.91721","url":null,"abstract":"We study characterizations of s-Σ-quasi-projective modules and properties of special star modules (tilting modules and Σ-quasi-projective self-generators) and characterize Σ-self-static star modules in terms of equivalences.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"496 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80152754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-10DOI: 10.35940/IJAC.B2003.101221
Shixaliyev Kerem Seyfi
{"title":"Methods of Modıfıcatıon of Used Polyolephınes","authors":"Shixaliyev Kerem Seyfi","doi":"10.35940/IJAC.B2003.101221","DOIUrl":"https://doi.org/10.35940/IJAC.B2003.101221","url":null,"abstract":"","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"1 1","pages":"14-18"},"PeriodicalIF":0.8,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49340003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-23DOI: 10.1142/s0218196723500492
P. Makienko, Carlos Cabrera
We compare dynamical and algebraic properties of semigroups of rational maps. In particular, we show a version of the Day-von Neumann's conjecture and give a partial positive answer to"Sushkievich's problem"for semigroups of rational maps. We also show the relation of these conjectures with Furstenberg's $times 2 times 3$ problem and prove a coarse version of Furstenberg's problem for semigroups of non-exceptional polynomials.
{"title":"On amenability and measure of maximal entropy for semigroups of rational maps: II","authors":"P. Makienko, Carlos Cabrera","doi":"10.1142/s0218196723500492","DOIUrl":"https://doi.org/10.1142/s0218196723500492","url":null,"abstract":"We compare dynamical and algebraic properties of semigroups of rational maps. In particular, we show a version of the Day-von Neumann's conjecture and give a partial positive answer to\"Sushkievich's problem\"for semigroups of rational maps. We also show the relation of these conjectures with Furstenberg's $times 2 times 3$ problem and prove a coarse version of Furstenberg's problem for semigroups of non-exceptional polynomials.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43717688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-16DOI: 10.1142/s0218196723500546
N. Ruškuc, B. Witt
A finite unary algebra $(A,F)$ has only countably many countable subdirect powers if and only if every operation $fin F$ is either a permutation or a constant mapping.
有限一元代数$（A，F）$只有可数多次可数次幂，当且仅当F$中的每个运算$F都是置换或常数映射。
{"title":"On the Number of Countable Subdirect Powers of Unary Algebras","authors":"N. Ruškuc, B. Witt","doi":"10.1142/s0218196723500546","DOIUrl":"https://doi.org/10.1142/s0218196723500546","url":null,"abstract":"A finite unary algebra $(A,F)$ has only countably many countable subdirect powers if and only if every operation $fin F$ is either a permutation or a constant mapping.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43452650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-10DOI: 10.35940/IJAC.B2002.041121
Shixaliyev Kerem Seyfi
In given work a scientific base compatibility of polymers, produced by industry have been studied by revealing of thermodynamically regularities of polymer mixtures. The most significant thermodynamic regularities of the mixtures of polyolefin , produced by industry and heterochained polymers have been revealed and on this base the scientific bases of their compatibility have been developed for creation of multicomponent compositional materials with given complex of operating properties.
{"title":"Thermodinamics and Mutual Distribution of Macromolecules in the Systems: ChlorineChlorocontaining Polymers","authors":"Shixaliyev Kerem Seyfi","doi":"10.35940/IJAC.B2002.041121","DOIUrl":"https://doi.org/10.35940/IJAC.B2002.041121","url":null,"abstract":"In given work a scientific base compatibility of polymers, produced by industry have been studied by revealing of thermodynamically regularities of polymer mixtures. The most significant thermodynamic regularities of the mixtures of polyolefin , produced by industry and heterochained polymers have been revealed and on this base the scientific bases of their compatibility have been developed for creation of multicomponent compositional materials with given complex of operating properties.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"1 1","pages":"1-6"},"PeriodicalIF":0.8,"publicationDate":"2021-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44392256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alperin’s Weight Conjecture for Blocks (AWCFB) suggests a currently unknown structure in Finite Group Modular Representation Theory. The Green Correspondence fails AWCFB for blocks of p-solvable groups. An important result of L. Barker uses a variant of the Green Correspondence to prove AWFCB for blocks of p-solvable groups. This variant suggests the possibility of further solutions to AWCFB. Let G be a finite group, let N be a normal subgroup of G and let b be a block of N that is covered by the block B of G. Our main results demonstrate that: for B it suffices to obtain a required variant of the Green Correspondence for the block of the stabilizer of b corresponding to B and if b is of defect zero, then it suffices to reduce to the group G/N . L. Barker’s proof of the AWCFB for p-solvable groups is an immediate consequence of our results. Mathematics Subject Classification: 20C20
{"title":"Some results on a variant of the Green correspondence with applications to Alperin's weight conjecture for blocks","authors":"M. E. Harris","doi":"10.12988/IJA.2021.91524","DOIUrl":"https://doi.org/10.12988/IJA.2021.91524","url":null,"abstract":"Alperin’s Weight Conjecture for Blocks (AWCFB) suggests a currently unknown structure in Finite Group Modular Representation Theory. The Green Correspondence fails AWCFB for blocks of p-solvable groups. An important result of L. Barker uses a variant of the Green Correspondence to prove AWFCB for blocks of p-solvable groups. This variant suggests the possibility of further solutions to AWCFB. Let G be a finite group, let N be a normal subgroup of G and let b be a block of N that is covered by the block B of G. Our main results demonstrate that: for B it suffices to obtain a required variant of the Green Correspondence for the block of the stabilizer of b corresponding to B and if b is of defect zero, then it suffices to reduce to the group G/N . L. Barker’s proof of the AWCFB for p-solvable groups is an immediate consequence of our results. Mathematics Subject Classification: 20C20","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":" 47","pages":"37-47"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72379163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the notion of relative coresolving subcategories and bounded Hom-projective generator and then give the Auslander-Reiten correspondence of Wakamatsu-silting complexes. Mathematics Subject Classification: 18G80; 16E35; 16G10
{"title":"The Auslander-Reiten correspondence of Wakamatsu-silting complexes","authors":"Weiqing Cao, Jiaqun Wei","doi":"10.12988/IJA.2021.91529","DOIUrl":"https://doi.org/10.12988/IJA.2021.91529","url":null,"abstract":"We introduce the notion of relative coresolving subcategories and bounded Hom-projective generator and then give the Auslander-Reiten correspondence of Wakamatsu-silting complexes. Mathematics Subject Classification: 18G80; 16E35; 16G10","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"34 1","pages":"103-109"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91286166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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