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International Journal of Group Theory最新文献

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On the relationships between the factors of the upper and lower central series in some non-periodic groups 若干非周期群上、下中心级数因子之间的关系
IF 0.2
International Journal of Group Theory Pub Date : 2016-12-20 DOI: 10.22108/IJGT.2017.21674
M. Dixon, L. A. Kurdachenko, I. Subbotin
{"title":"On the relationships between the factors of the upper and lower central series in some non-periodic groups","authors":"M. Dixon, L. A. Kurdachenko, I. Subbotin","doi":"10.22108/IJGT.2017.21674","DOIUrl":"https://doi.org/10.22108/IJGT.2017.21674","url":null,"abstract":"This paper deals with the mutual relationships between the factor group G/ζ(G) (respectively G/ζk(G)) and G ′ (respectively γk+1(G) and G ). It is proved that if G/ζ(G) (respectively G/ζk(G)) has finite 0-rank, then G ′ (respectively γk+1(G) and G ) also have finite 0-rank. Furthermore, bounds for the 0-ranks of G′, γk+1(G) and G N are obtained.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"7 1","pages":"37-50"},"PeriodicalIF":0.2,"publicationDate":"2016-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205735","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
A note on transfer theorems 关于转移定理的注解
IF 0.2
International Journal of Group Theory Pub Date : 2016-12-01 DOI: 10.22108/IJGT.2016.9851
Haoran Yu
{"title":"A note on transfer theorems","authors":"Haoran Yu","doi":"10.22108/IJGT.2016.9851","DOIUrl":"https://doi.org/10.22108/IJGT.2016.9851","url":null,"abstract":"‎In this paper‎, ‎we generalize some transfer theorems‎. ‎In particular‎, ‎we derive one of‎ ‎the main results of Gagola (Contemp Math.‎, ‎524 (2010) 49-60) from our results‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"47-52"},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205546","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
A NOTE ON THE COPRIME GRAPH OF A GROUP 关于群的素数图的注释
IF 0.2
International Journal of Group Theory Pub Date : 2016-12-01 DOI: 10.22108/IJGT.2016.9125
H. Dorbidi
{"title":"A NOTE ON THE COPRIME GRAPH OF A GROUP","authors":"H. Dorbidi","doi":"10.22108/IJGT.2016.9125","DOIUrl":"https://doi.org/10.22108/IJGT.2016.9125","url":null,"abstract":"In this paper we study the coprime graph of a group G. The coprime graph of a group G, denoted by G, is a graph whose vertices are elements of G and two distinct vertices x and y are adjacent if and only if ( jxj;jyj) = 1. In this paper, we show that ( G) = !( G) : We classify all the groups which G is a complete r partite graph or a planar graph. Also we study the automorphism group of G.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"17-22"},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205494","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: 15
CONJUGACY SEPARABILITY OF CERTAIN HNN EXTENSIONS WITH NORMAL ASSOCIATED SUBGROUPS 某些具有正相关子群的HNN扩展的共轭可分性
IF 0.2
International Journal of Group Theory Pub Date : 2016-12-01 DOI: 10.22108/IJGT.2016.9021
K. B. Wong, D. Robinson, P. C. Wong
{"title":"CONJUGACY SEPARABILITY OF CERTAIN HNN EXTENSIONS WITH NORMAL ASSOCIATED SUBGROUPS","authors":"K. B. Wong, D. Robinson, P. C. Wong","doi":"10.22108/IJGT.2016.9021","DOIUrl":"https://doi.org/10.22108/IJGT.2016.9021","url":null,"abstract":"In this paper, we will give necessary and sufficient conditions for certain HNN extensions of subgroup separable groups with normal associated subgroup to be conjugacy separable. In fact, we will show that these HNN extensions are conjugacy separable if and only if the normalizer of one of its associated subgroup is conjugacy separable.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"1-16"},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205375","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
A remark on group rings of periodic groups 关于周期群的群环的注解
IF 0.2
International Journal of Group Theory Pub Date : 2016-12-01 DOI: 10.22108/IJGT.2016.9425
A. Grigoryan
{"title":"A remark on group rings of periodic groups","authors":"A. Grigoryan","doi":"10.22108/IJGT.2016.9425","DOIUrl":"https://doi.org/10.22108/IJGT.2016.9425","url":null,"abstract":"A positive solution of the problem of the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of sufficiently large odd periods","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"23-25"},"PeriodicalIF":0.2,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205504","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 groups with specified quotient power graphs 关于具有指定商幂图的群
IF 0.2
International Journal of Group Theory Pub Date : 2016-09-01 DOI: 10.22108/IJGT.2016.8542
Mostafa Shaker, M. Iranmanesh
{"title":"On groups with specified quotient power graphs","authors":"Mostafa Shaker, M. Iranmanesh","doi":"10.22108/IJGT.2016.8542","DOIUrl":"https://doi.org/10.22108/IJGT.2016.8542","url":null,"abstract":"In this paper we study some relations between the power and quotient power graph of a nite group. These interesting relations motivate us to nd some graph theoretical properties of the quotient power graph and the proper quotient power graph of a nite group G. In addition, we classify those groups whose quotient (proper quotient) power graphs are isomorphic to trees or paths.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"49-60"},"PeriodicalIF":0.2,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205652","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
Normal edge-transitive and $frac{1}{2}-$arc$-$transitive Cayley graphs on non-abelian groups of order $2pq$, $p > q$ are odd primes $2pq$， $p > q$阶非阿贝尔群上的正常边传递和$ frc b{1}{2}-$arc$-$传递Cayley图是奇素数
IF 0.2
International Journal of Group Theory Pub Date : 2016-09-01 DOI: 10.22108/IJGT.2016.6537
A. Ashrafi, B. Soleimani
{"title":"Normal edge-transitive and $frac{1}{2}-$arc$-$transitive Cayley graphs on non-abelian groups of order $2pq$, $p > q$ are odd primes","authors":"A. Ashrafi, B. Soleimani","doi":"10.22108/IJGT.2016.6537","DOIUrl":"https://doi.org/10.22108/IJGT.2016.6537","url":null,"abstract":"Darafsheh and Assari in [Normal edge-transitive Cayley graphs on non-abelian groups of order 4p, where p is a prime number, Sci. China Math. 56 (1) (2013) 213 219.] classied the connected normal edge transitive and 1 arc-transitive Cayley graph of groups of order 4p. In this paper we continue this work by classifying the connected Cayley graph of groups of order 2pq, p > q are primes. As a consequence it is proved that Cay(G;S) is a 1 edgetransitive Cayley graph of order 2pq, p > q if and only if jSj is an even integer greater than 2, S = T[ T 1 and T f cba i j 0 i p 1g such that T and T 1 are orbits of Aut(G;S) and","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"1-8"},"PeriodicalIF":0.2,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68204875","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
Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes 无限秩的固有子群具有有限多环共轭类的群
IF 0.2
International Journal of Group Theory Pub Date : 2016-09-01 DOI: 10.22108/IJGT.2016.8776
Mounia Bouchelaghem, N. Trabelsi
{"title":"Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes","authors":"Mounia Bouchelaghem, N. Trabelsi","doi":"10.22108/IJGT.2016.8776","DOIUrl":"https://doi.org/10.22108/IJGT.2016.8776","url":null,"abstract":"A group $G$ is said to be a $(PF)C$-group or to have polycyclic-by-finite conjugacy classes, if $G/C_{G}(x^{G})$ is a polycyclic-by-finite group for all $xin G$. This is a generalization of the familiar property of being an $FC$-group. De Falco et al. (respectively, de Giovanni and Trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. Here we consider groups whose proper subgroups of infinite rank are $(PF)C$-groups and we prove that if $G$ is a group of infinite rank having a non-trivial finite or abelian factor group and if all proper subgroups of $G$ of infinite rank are $(PF)C$-groups, then so is $G$. We prove also that if $G$ is a locally soluble-by-finite group of infinite rank which has no simple homomorphic images of infinite rank and whose proper subgroups of infinite rank are $(PF)C$-groups, then so are all proper subgroups of $G$.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"61-67"},"PeriodicalIF":0.2,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205249","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
Conjugate $p$-elements of full support that generate the wreath product $C_{p}wr C_{p}$ 共轭$p$-生成环积$C_{p}wr C_{p}$的全支持元素
IF 0.2
International Journal of Group Theory Pub Date : 2016-09-01 DOI: 10.22108/IJGT.2016.7806
David Ward
{"title":"Conjugate $p$-elements of full support that generate the wreath product $C_{p}wr C_{p}$","authors":"David Ward","doi":"10.22108/IJGT.2016.7806","DOIUrl":"https://doi.org/10.22108/IJGT.2016.7806","url":null,"abstract":"For a symmetric group G:=symn\">G:=symnG:=symn and a conjugacy class X\">XX of involutions in G\">GG‎, ‎it is known that if the class of involutions does not have a unique fixed point‎, ‎then‎ - ‎with a few small exceptions‎ - ‎given two elements a,x∈X\">a,x∈Xa,x∈X‎, ‎either ⟨a,x⟩\">⟨a,x⟩⟨a,x⟩ is isomorphic to the dihedral group D8\">D8D8‎, ‎or there is a further element y∈X\">y∈Xy∈X such that ⟨a,y⟩≅⟨x,y⟩≅D8\">⟨a,y⟩≅⟨x,y⟩≅D8⟨a,y⟩≅⟨x,y⟩≅D8 (P‎. ‎Rowley and D‎. ‎Ward‎, ‎On π\">ππ-Product Involution Graphs in Symmetric‎ ‎Groups‎. ‎MIMS ePrint‎, ‎2014)‎.  ‎One natural generalisation of this to p\">pp-elements is to consider when two conjugate p\">pp-elements generate a wreath product of two cyclic groups of order p\">pp‎. ‎In this paper we give necessary and sufficient conditions for this in the case that our p\">pp-elements have full support‎. ‎These conditions relate to given matrices that are of circulant or permutation type‎, ‎and corresponding polynomials that represent these matrices‎. ‎We also consider the case that the elements do not have full support‎, ‎and see why generalising our results to such elements would not be a natural generalisation‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"9-35"},"PeriodicalIF":0.2,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68205180","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 THE COMMUTATIVITY DEGREE IN FINITE MOUFANG LOOPS 有限牟方环的交换度
IF 0.2
International Journal of Group Theory Pub Date : 2016-09-01 DOI: 10.22108/IJGT.2016.8477
K. Ahmadidelir
{"title":"ON THE COMMUTATIVITY DEGREE IN FINITE MOUFANG LOOPS","authors":"K. Ahmadidelir","doi":"10.22108/IJGT.2016.8477","DOIUrl":"https://doi.org/10.22108/IJGT.2016.8477","url":null,"abstract":"‎The commutativity degree‎, ‎Pr(G)\">Pr(G)Pr(G)‎, ‎of a finite group G\">GG (i.e‎. ‎the probability that two (randomly chosen) elements of G\">GGcommute with respect to its operation)) has been studied well by many authors‎. ‎It is well-known that the best upper bound for Pr(G)\">Pr(G)Pr(G) is 58\">5858 for a finite non-abelian group G\">GG‎.  ‎In this paper‎, ‎we will define the same concept for a finite non--abelian Moufang loop M\">MM and try to give a best upper bound for Pr(M)\">Pr(M)Pr(M)‎. ‎We will prove that for a well-known class of finite Moufang loops‎, ‎named Chein loops‎, ‎and its modifications‎, ‎this best upper bound is 2332\">23322332‎. ‎So‎, ‎our conjecture is that for any finite Moufang loop M\">MM‎, ‎Pr(M)≤2332\">Pr(M)≤2332Pr(M)≤2332‎.   ‎Also‎, ‎we will obtain some results related to the Pr(M)\">Pr(M)Pr(M) and ask the similar questions raised and answered in group theory about the relations between the structure of a finite group and its commutativity degree in finite Moufang loops‎.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":"5 1","pages":"37-47"},"PeriodicalIF":0.2,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68204979","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
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