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International Journal of Group Theory最新文献

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On algebraic geometry over completely simple semigroups 关于完全简单半群上的代数几何
IF 0.2
International Journal of Group Theory Pub Date : 2017-10-21 DOI: 10.22108/IJGT.2017.21975
A. Shevlyakov
{"title":"On algebraic geometry over completely simple semigroups","authors":"A. Shevlyakov","doi":"10.22108/IJGT.2017.21975","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21975","url":null,"abstract":"We study equations over completely simple semigroups and describe the coordinate semigroups of irreducible algebraic sets for such semigroups.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49615447","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}
引用次数: 1
One-prime power hypothesis for conjugacy class sizes 共轭类大小的一素数幂假设
IF 0.2
International Journal of Group Theory Pub Date : 2017-09-01 DOI: 10.22108/IJGT.2017.12043
A. Camina, R. Camina
{"title":"One-prime power hypothesis for conjugacy class sizes","authors":"A. Camina, R. Camina","doi":"10.22108/IJGT.2017.12043","DOIUrl":"https://doi.org/10.22108/IJGT.2017.12043","url":null,"abstract":"A finite group $G$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition is isomorphic to $S times A$ where $A$ is abelian and $S cong PSL_2(q)$ for $q in {4,8}$. We confirm this conjecture.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42688540","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}
引用次数: 0
An infinite family of finite $2$-groups with deficiency zero 具有亏零的有限$2$群的无限族
IF 0.2
International Journal of Group Theory Pub Date : 2017-09-01 DOI: 10.22108/IJGT.2017.21213
H. Abdolzadeh, Reza Sabzchi
{"title":"An infinite family of finite $2$-groups with deficiency zero","authors":"H. Abdolzadeh, Reza Sabzchi","doi":"10.22108/IJGT.2017.21213","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21213","url":null,"abstract":"‎‎We determine a new infinite sequence of finite $2$-groups with deficiency zero‎. ‎The groups have $2$ generators and $2$ relations‎, ‎they have coclass $3$‎ ‎and they are not metacyclic‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41285545","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}
引用次数: 2
Transitive $t$-designs and strongly regular graphs constructed from linear groups $L(2,q)$, $q leq 23$ 由线性群$L(2,q)$， $q leq 23$构造的传递$t$-设计和强正则图
IF 0.2
International Journal of Group Theory Pub Date : 2017-08-17 DOI: 10.22108/IJGT.2017.21613
D. Crnković, Andrea Švob
{"title":"Transitive $t$-designs and strongly regular graphs constructed from linear groups $L(2,q)$, $q leq 23$","authors":"D. Crnković, Andrea Švob","doi":"10.22108/IJGT.2017.21613","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21613","url":null,"abstract":"‎In this paper we construct transitive $t$-designs from the linear groups $L(2,q)‎, ‎q leq 23$‎. ‎Thereby we classify $t$-designs‎, ‎$t ge 2$‎, ‎admitting a transitive action of the linear groups $L(2,q)‎, ‎q leq 23$‎, ‎up to 35 points and obtained numerous transitive designs‎, ‎for $36leq vleq 55$‎. ‎In many cases we proved the existence of $t$-designs with certain parameter sets‎. ‎Among others we constructed $t$-designs with parameters $2$-$(55,10,4)$‎, ‎$3$-$(24,11,495)$‎, ‎$3$-$(24,12‎, ‎5m)‎, ‎m in {11‎, ‎12,22‎, ‎33‎, ‎44‎, ‎66‎, ‎132}$‎. ‎Furthermore‎, ‎we constructed strongly regular graphs admitting a transitive action of the linear groups $L(2,q)‎, ‎q leq 23$‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47440469","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}
引用次数: 1
Sylow multiplicities in finite groups 有限群中的Sylow乘法
IF 0.2
International Journal of Group Theory Pub Date : 2017-06-09 DOI: 10.22108/IJGT.2017.21482
D. Levy
{"title":"Sylow multiplicities in finite groups","authors":"D. Levy","doi":"10.22108/IJGT.2017.21482","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21482","url":null,"abstract":"","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41380259","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}
引用次数: 0
On the dimension of the product $[L_2,L_2,L_1]$ in free Lie algebras 关于自由李代数中乘积$[L_2，L_2，L_1]$的维数
IF 0.2
International Journal of Group Theory Pub Date : 2017-06-09 DOI: 10.22108/IJGT.2017.21481
Nil Mansuroğlu
{"title":"On the dimension of the product $[L_2,L_2,L_1]$ in free Lie algebras","authors":"Nil Mansuroğlu","doi":"10.22108/IJGT.2017.21481","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21481","url":null,"abstract":"Let $L$ be a free Lie algebra of rank $rgeq2$ over a field $F$ and let $L_n$ denote the degree $n$ homogeneous component of $L$‎. ‎By using the dimensions of the corresponding homogeneous and fine homogeneous components of the second derived ideal of free centre-by-metabelian Lie algebra over a field $F$‎, ‎we determine the dimension of $[L_2,L_2,L_1]$‎. ‎Moreover‎, ‎by this method‎, ‎we show that the dimension of $[L_2,L_2,L_1]$ over a field of characteristic $2$ is different from the dimension over a field of characteristic other than $2$.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46336082","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}
引用次数: 0
Induced operators on symmetry classes of polynomials 多项式对称类上的诱导算子
IF 0.2
International Journal of Group Theory Pub Date : 2017-06-01 DOI: 10.22108/IJGT.2017.12406
Mahin Ranjbari, Y. Zamani
{"title":"Induced operators on symmetry classes of polynomials","authors":"Mahin Ranjbari, Y. Zamani","doi":"10.22108/IJGT.2017.12406","DOIUrl":"https://doi.org/10.22108/IJGT.2017.12406","url":null,"abstract":"‎‎In this paper‎, ‎we give a necessary and sufficient condition for the equality of two symmetrized decomposable polynomials‎. ‎Then‎, ‎we study some algebraic and geometric properties of the induced operators over symmetry classes of polynomials in the case of linear characters‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45438156","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}
引用次数: 4
Converse of Lagrange's theorem (CLT) numbers under $1000$ 1000美元下拉格朗日定理（CLT）数的逆$
IF 0.2
International Journal of Group Theory Pub Date : 2017-06-01 DOI: 10.22108/IJGT.2017.13314
J. B. Nganou
{"title":"Converse of Lagrange's theorem (CLT) numbers under $1000$","authors":"J. B. Nganou","doi":"10.22108/IJGT.2017.13314","DOIUrl":"https://doi.org/10.22108/IJGT.2017.13314","url":null,"abstract":"A positive integer $n$ is called a CLT number if every group of order $n$ satisfies the converse of Lagrange's Theorem‎. ‎In this note‎, ‎we find all CLT and supersolvable numbers up to $1000$‎. ‎We also formulate some questions about the distribution of these numbers‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47100518","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}
引用次数: 5
A note on finite groups with the indice of some maximal subgroups being primes 关于一些极大子群的标记为素数的有限群的一个注记
IF 0.2
International Journal of Group Theory Pub Date : 2017-06-01 DOI: 10.22108/IJGT.2017.12396
Cui Zhang
{"title":"A note on finite groups with the indice of some maximal subgroups being primes","authors":"Cui Zhang","doi":"10.22108/IJGT.2017.12396","DOIUrl":"https://doi.org/10.22108/IJGT.2017.12396","url":null,"abstract":"‎The Theorem 12 in [A note on‎ ‎$p$-nilpotence and solvability of finite groups‎, ‎J‎. ‎Algebra 321‎ ‎(2009) 1555--1560.] investigated the non-abelian simple groups in‎ ‎which some maximal subgroups have primes indices‎. ‎In this note we‎ ‎show that this result can be applied to prove that the finite groups‎ ‎in which every non-nilpotent maximal subgroup has prime index are‎ ‎solvable‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45546099","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}
引用次数: 0
Nonnilpotent subsets in the Suzuki groups Suzuki群中的非幂零子集
IF 0.2
International Journal of Group Theory Pub Date : 2017-06-01 DOI: 10.22108/IJGT.2017.11176
M. Zarrin
{"title":"Nonnilpotent subsets in the Suzuki groups","authors":"M. Zarrin","doi":"10.22108/IJGT.2017.11176","DOIUrl":"https://doi.org/10.22108/IJGT.2017.11176","url":null,"abstract":"Let $G$ be a group and $mathcal{N}$ be the class of all nilpotent groups. A subset $A$ of $G$ is said to be nonnilpotent if for any two distinct elements $a$ and $b$ in $A$, $langle a, brangle notin mathcal{N}$. If, for any other nonnilpotent subset $B$ in $G$, $|A|geq |B|$, then $A$ is said to be a maximal nonnilpotent subset and the cardinality of this subset (if it exists) is denoted by $omega(mathcal{N}_G)$. In this paper, among other results, we obtain $omega(mathcal{N}_{Suz(q)})$ and $omega(mathcal{N}_{PGL(2,q)})$, where $Suz(q)$ is the Suzuki simple group over the field with $q$ elements and $PGL(2,q)$ is the projective general linear group of degree $2$ over the finite field with $q$ elements, respectively.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46382699","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}
引用次数: 0
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