Abstract
A subgroup H of a group G is said to be self-conjugate-permutable if HHx=HxH implies Hx=H for any x of G.A finite group G is called an SC-group(PSC-group,respectively)if all cyclic subgroups of G of order 2 or order 4(prime order or order 4,respectively)are self-conjugate-permutable in G.In this paper,we first investigate the structure of finite non-solvable groups all of whose second maximal subgroups are SC-groups;then we mainly investigate the structure of finite groups in which all of maximal subgroups of even order are PSC-groups.In fact,we describe the structure of finite groups which are not PSC-groups but all of whose maximal subgroups of even order are PSC-groups.
基金项目
National Natural Science Foundation of China(12061030)
Natural Science Foundation of Hainan Province(122RC652)
NETL
NSTL
万方数据