Local Covering Subgroups in Finite Groups  

作　　者：Guo Hua QIAN 

机构地区：[1]Department of Mathematics,Changshu Institute of Technology,Changshu 215500,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第5期768-774,共7页数学学报（英文版）

基　　金：Supported by the NSF of China(Grant No.11871011)。

摘　　要：A subgroup A of a finite group G is called a local covering subgroup of G if A^(G)=AB for all maximal G-invariant subgroup B of A^(G)=(A^(G),g∈G).Let p be a prime and d be a positive integer.Assume that all subgroups of p^(d),and all cyclic subgroups of order 4 when p^(d)=2 and a Sylow2-subgroup of G is nonabelian,of G are local covering subgroups.Then G is p-supersolvable whenever p^(d)=p or p^(d)≤(√|G|_(p))or p^(d)≤|O_(p'p)(G)|_(p)/p.

关 键 词：Finite group local covering subgroup p-supersolvable group 

分 类 号：O152.1[理学—数学]