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International Journal of Group Theory最新文献

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Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements Chevalley群$G_{2}（5）$的同序元数集刻画
IF 0.2
International Journal of Group Theory Pub Date : 2022-03-01 DOI: 10.22108/IJGT.2021.120906.1594
M. Jahandideh, M. Darafsheh
{"title":"Characterization of the Chevalley group $G_{2}(5)$ by the set of numbers of the same order elements","authors":"M. Jahandideh, M. Darafsheh","doi":"10.22108/IJGT.2021.120906.1594","DOIUrl":"https://doi.org/10.22108/IJGT.2021.120906.1594","url":null,"abstract":"Let $G$ be a group and $omega(G)={o(g)|gin G}$ be the set of element orders of $G$. Let $kinomega(G)$ and $s_{k}=|{gin G|o(g)=k}|$. Let $nse(G)={s_{k}|kinomega(G)}.$ In this paper, we prove that if $G$ is a group and $G_{2}(5)$ is the Chevalley simple group of type $G_{2}$ over $GF(5)$ such that $nse(G)=nse(G_{2}(5))$, then $Gcong G_{2}(5)$.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43066884","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
Some results on the join graph of finite groups 关于有限群连接图的一些结果
IF 0.2
International Journal of Group Theory Pub Date : 2021-12-01 DOI: 10.22108/IJGT.2020.123287.1625
Zahara Bahrami, B. Taeri
{"title":"Some results on the join graph of finite groups","authors":"Zahara Bahrami, B. Taeri","doi":"10.22108/IJGT.2020.123287.1625","DOIUrl":"https://doi.org/10.22108/IJGT.2020.123287.1625","url":null,"abstract":"‎Let $G$ be a finite group which is not cyclic of prime power order‎. ‎The join graph $Delta(G)$ of $G$ is a graph whose vertex set is the set of all proper subgroups of $G$‎, ‎which are not contained in the Frattini subgroup $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $G=langle H‎, ‎Krangle$‎. ‎Among other results‎, ‎we show that if $G$ is a finite cyclic group and $H$ is a finite group such that $Delta(G)congDelta(H)$‎, ‎then $H$ is cyclic‎. ‎Also we prove that $Delta(G)congDelta(A_5)$ if and only if $Gcong A_5$‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46457834","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 probability of zero divisor elements in group rings 群环中零因子元素的概率
IF 0.2
International Journal of Group Theory Pub Date : 2021-10-25 DOI: 10.22108/IJGT.2021.126694.1664
M. Salih, M. Haval
{"title":"On the probability of zero divisor elements in group rings","authors":"M. Salih, M. Haval","doi":"10.22108/IJGT.2021.126694.1664","DOIUrl":"https://doi.org/10.22108/IJGT.2021.126694.1664","url":null,"abstract":"Let R be a non trivial finite commutative ring with identity and G be a non trivial\u0000group. We denote by P(RG) the probability that the product of two randomly chosen\u0000elements of a finite group ring RG is zero. We show that P(RG) <0.25 if and only if\u0000RG is not isomorphic to Z2C2, Z3C2, Z2C3. Furthermore, we give the upper bound and lower bound for\u0000P(RG). In particular, we present the general formula for P(RG), where R is a finite field of\u0000characteristic p and |G| ≤ 4.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44489952","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
On Co-Maximal Subgroup Graph of $Z_n$ 关于$Z_n的共极大子群图$
IF 0.2
International Journal of Group Theory Pub Date : 2021-09-29 DOI: 10.22108/IJGT.2021.129788.1732
M. Saha, Sucharita Biswas, Angsuman Das
{"title":"On Co-Maximal Subgroup Graph of $Z_n$","authors":"M. Saha, Sucharita Biswas, Angsuman Das","doi":"10.22108/IJGT.2021.129788.1732","DOIUrl":"https://doi.org/10.22108/IJGT.2021.129788.1732","url":null,"abstract":"The co-maximal subgroup graph $Gamma(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK = G$. In this paper, we study and characterize various properties like diameter, domination number, perfectness, hamiltonicity, etc. of $Gamma(mathbb{Z}_n)$.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42730354","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
Infinite Locally Finite Simple Groups with Many Complemented Subgroups 具有许多补子群的无限局部有限单群
IF 0.2
International Journal of Group Theory Pub Date : 2021-09-24 DOI: 10.22108/IJGT.2021.129515.1700
M. Ferrara, M. Trombetti
{"title":"Infinite Locally Finite Simple Groups with Many Complemented Subgroups","authors":"M. Ferrara, M. Trombetti","doi":"10.22108/IJGT.2021.129515.1700","DOIUrl":"https://doi.org/10.22108/IJGT.2021.129515.1700","url":null,"abstract":"We prove that the following families of (infinite) groups have complemented subgroup lattice‎: ‎alternating groups‎, ‎finitary symmetric groups‎, ‎Suzuki groups over an infinite locally finite field of characteristic $2$‎, ‎Ree groups over an infinite locally finite field of characteristic~$3$‎. ‎We also show that if the Sylow primary subgroups of a locally finite simple group $G$ have complemented subgroup lattice‎, ‎then this is also the case for $G$‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42566725","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 a result of nilpotent subgroups of solvable groups 关于可解群的幂零子群的一个结果
IF 0.2
International Journal of Group Theory Pub Date : 2021-09-24 DOI: 10.22108/IJGT.2021.128455.1690
Yong Yang
{"title":"On a result of nilpotent subgroups of solvable groups","authors":"Yong Yang","doi":"10.22108/IJGT.2021.128455.1690","DOIUrl":"https://doi.org/10.22108/IJGT.2021.128455.1690","url":null,"abstract":"‎Heineken [‎H‎. ‎Heineken‎, ‎Nilpotent subgroups of finite soluble groups‎, Arch‎. ‎Math.(Basel)‎, ‎ 56 no‎. ‎5 (1991) 417--423‎.] studied the order of the nilpotent subgroups of the largest order of a solvable group‎. ‎We point out an error‎, ‎and thus refute the proof of the main result of [‎H‎. ‎Heineken‎, ‎Nilpotent subgroups of finite soluble groups‎, Arch‎. ‎Math.(Basel)}‎, 56 no‎. ‎5 (1991) 417--423‎.].","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43049801","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
Parameters of the coprime graph of a group 群的素图参数
IF 0.2
International Journal of Group Theory Pub Date : 2021-09-01 DOI: 10.22108/IJGT.2020.112121.1489
Jessica Hamm, A. Way
{"title":"Parameters of the coprime graph of a group","authors":"Jessica Hamm, A. Way","doi":"10.22108/IJGT.2020.112121.1489","DOIUrl":"https://doi.org/10.22108/IJGT.2020.112121.1489","url":null,"abstract":"‎There are many different graphs one can associate to a group‎. ‎Some examples are the well-known Cayley graph‎, ‎the zero divisor graph (of a ring)‎, ‎the power graph‎, ‎and the recently introduced coprime graph of a group‎. ‎The coprime graph of a group $G$‎, ‎denoted $Gamma_G$‎, ‎is the graph whose vertices are the group elements with $g$ adjacent to $h$ if and only if $(o(g),o(h))=1$‎. ‎In this paper we calculate the independence number of the coprime graph of the dihedral groups‎. ‎Additionally‎, ‎we characterize the groups whose coprime graph is perfect‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46494227","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: 3
ON THE AUTOMORPHISM GROUPS OF SOME LEIBNIZ ALGEBRAS 一些莱布尼兹代数的自同构群
IF 0.2
International Journal of Group Theory Pub Date : 2021-08-15 DOI: 10.22108/IJGT.2021.130057.1735
L. A. Kurdachenko, A. A. Pypka, I. Subbotin
{"title":"ON THE AUTOMORPHISM GROUPS OF SOME LEIBNIZ ALGEBRAS","authors":"L. A. Kurdachenko, A. A. Pypka, I. Subbotin","doi":"10.22108/IJGT.2021.130057.1735","DOIUrl":"https://doi.org/10.22108/IJGT.2021.130057.1735","url":null,"abstract":"We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46187140","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
On efficient presentations of the groups $text{PSL}(2,m)$ 组$text{PSL}(2,m)$的有效表示
IF 0.2
International Journal of Group Theory Pub Date : 2021-07-14 DOI: 10.22108/IJGT.2021.128791.1696
O. Stoytchev
{"title":"On efficient presentations of the groups $text{PSL}(2,m)$","authors":"O. Stoytchev","doi":"10.22108/IJGT.2021.128791.1696","DOIUrl":"https://doi.org/10.22108/IJGT.2021.128791.1696","url":null,"abstract":"dWe exhibit presentations of the Von Dyck groups $D(2, 3, m)‎, ‎ mge 3$‎, ‎in terms of two generators of order $m$ satisfying three relations‎, ‎one of which is Artin's braid relation‎. ‎By dropping the relation which fixes the order of the generators we obtain the universal covering groups of the corresponding Von Dyck groups‎. ‎In the cases $m=3, ‎‎4, 5$‎, ‎these are respectively the double covers of the finite rotational tetrahedral‎, ‎octahedral and icosahedral groups‎. ‎When $mge 6$ we obtain infinite covers of the corresponding infinite Von Dyck groups‎. ‎The interesting cases arise for $mge 7$ when these groups act as discrete groups of isometries of the hyperbolic plane‎. ‎Imposing a suitable third relation we obtain three-relator presentations of $text{PSL}(2,m)$‎. ‎We discover two general formulas presenting these as factors of $D(2, 3, m)$‎. ‎The first one works for any odd $m$ and is essentially equivalent to the shortest known presentation of Sunday cite{Sunday}‎. ‎The second applies to the cases $mequivpm 2 (text{mod} 3)$‎, ‎$m ≢ 11(text{mod} 30)$‎, ‎and is substantively shorter‎. ‎Additionally‎, ‎by random search‎, ‎we find many efficient presentations of‎ ‎finite simple Chevalley groups PSL($2,q$) as factors of $D(2, 3, m)$ where $m$ divides the order of the group‎. ‎The only other simple group that we found in this way is the sporadic Janko group $J_2$‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47396658","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
New Lower Bounds for the Number of Conjugacy Classes in Finite Nilpotent Groups 有限幂零群中共轭类数的新下界
IF 0.2
International Journal of Group Theory Pub Date : 2021-07-10 DOI: 10.22108/IJGT.2021.128396.1687
E. Bertram
{"title":"New Lower Bounds for the Number of Conjugacy Classes in Finite Nilpotent Groups","authors":"E. Bertram","doi":"10.22108/IJGT.2021.128396.1687","DOIUrl":"https://doi.org/10.22108/IJGT.2021.128396.1687","url":null,"abstract":"P.Hall's classical equality for the number of conjugacy classes in p-groups yields k(G) >= (3/2)log_2 |G|when G is nilpotent. Using only Hall's theorem, this is the best one can do when |G| = 2^n. Using aresult of G.J. Sherman, we improve the constant 3/2 to 5/3, which is best possible across all nilpotentgroups and to 15/8 when G is nilpotent and |G| is not equal to 8 or 16. These results are then used to prove that k(G) > log_3 |G| when G/N is nilpotent, under natural conditions on N (normal in) G. Also,when G' is nilpotent of class c, we prove that k(G) >= (log |G|)^t when |G| is large enough, dependingonly on (c,t).","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2021-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205313","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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