SUBGROUPS

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Maximal Subgroups in the Classical Groups Normalizing Solvable Subgroups
《Algebra Colloquium》2021年第2期181-194,共14页Xin Hou Shangzhi Li Yucheng Yang Jiping Zhang 
funded by Scientific Research Project of Beijing Educational Committee(No.KM202110028004).
Let G be a classical group over an arbitrary field F,acting on an n-dimensional F-space V=V(n,F).All those maximal subgroups of G are classified each of which normalizes a solvable subgroup N of GL(V/F)not lying in F^...
关键词：classical group over arbitrary field maximal subgroup solvable subgroup 
On a Graph Related to Subgroups Generated by a Conjugacy Class in Finite Groups
《Algebra Colloquium》2020年第2期193-198,共6页S.M.Robati 
Let G be a group,and let →/ΓC(G) be a digraph whose vertices are the nontrivial conjugacy classes of G and there is an arc from a vertex C to a vertex C' if and only if C≠C' and(C)■(C').In this paper,we characteri...
关键词：conjugacy classes POSETS GRAPHS finite groups 
On Nearly σ-Embedded Subgroups of Finite Groups
《Algebra Colloquium》2019年第4期677-688,共12页Muhammad Tanveer Hussain Chenchen Cao Li Zhang AAIvanov 
Let G be a finite group,σ={σi|i∈ I}be some partition of the set of all primes and σ(G)={(σi|σi∩ π(G)≠0}.We say that a subgroup H of G is nearly cr-cmbcdded in G if there exists a cr-permutable subgroup T of G...
关键词：finite group cr-permutable subgroup cr-permutably embedded subgroup nearly cr-embedded subgroup supersoluble group 
A Characterization of PSL(2,q),q=5,7
《Algebra Colloquium》2019年第4期561-564,共4页Marius Tarnauceanu Jiping Zhang 
In this short note we prove that the finite non-abelian simple groups PSL(2,q),where g=5,7,are determincd by their posets of classes of isomorphic subgroups.Several interesting open problems are also formulated.
关键词：simple groups solvable groups posets of isomorphic subgroups 
Finite p-Groups Whose Number of Subgroups of Each Order Is at most p^4
《Algebra Colloquium》2019年第3期411-424,共14页Lifang Wang 
Assume G is a group of order p^n,where p is an odd prime.Let sk(G)denote the number of subgroups of order p^k of G.We give a criterion for a p-group to be with sk(G)≤p^4 for each integer k satisfying 1≤k≤n.Moreover...
关键词：finite P-GROUPS ENUMERATION of SUBGROUPS type of REGULAR P-GROUPS 
Finite p-Groups Whose Subgroups of Given Order are Isomorphic and Minimal Non-abelian被引量：1
《Algebra Colloquium》2019年第1期1-8,共8页Qinhai Zhang 
Finite p-groups whose subgroups of given order are isomorphic and minimal non-abelian are classified. In addition, two results on a chain condition of At-groups are improved.
关键词：metacyclic P-GROUPS At-groups chain condition of At-groups 
The McKay Conjecture for Finite Groups with Abelian Sylow 3-Subgroups被引量：1
《Algebra Colloquium》2017年第2期181-194,共14页Zhicheng Feng Conghui Li Zhenye Li 
In this paper, we prove that the McKay conjecture holds for finite groups with abelian Sylow 3-subgroups and any prime l via the inductive McKay condition.2010 Mathematics Subject Classification： 20C15, 20C33
关键词：McKay conjecture abelian Sylow 3-subgroups inductive McKay condition 
Gradewise Properties of Subgroups and Their Applications
《Algebra Colloquium》2017年第2期255-266,共12页Wenbin Guo Alexander N. Skiba 
For each finite group E, let O（E） be a binary relation on the set of all subgroups of E. If A and B are subgroups of a finite group G, then we say that the pair （A, B） enjoys the gradewise property （resp., genera...
关键词：finite group subgroup functor subgroup bifunctor gradewise property 
A Note on TI-Subgroups of a Finite Group被引量：2
《Algebra Colloquium》2014年第2期343-346,共4页Jiangtao Shi Cui Zhang 
The first author was supported by NSFC （Grant 11201401） and the China Postdoctoral Science Foundation （Grant 201104027）. The second author was supported by H.C. Orsted Postdoctoral Fellowship at DTU （Technical University of Denmark）.
Let G be a finite group and H a subgroup of G. Recall that H is said to be aTI-subgroup ofG ifHg∩H = 1 or H for each b∈ G. In this note, we prove that if all non-nilpotent subgroups of a finite non-nilpotent group G...
关键词：finite group non-nilpotent subgroup TI-subgroup NORMAL 
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