A generalized CAP-subgroup of a finite group

作者：Guo WenBin^*; Alexander Skiba N; Yang NanYing

来源：Science China Mathematics, 2015, 58(10): 2133-2144.

DOI：10.1007/s11425-015-5005-5

• finite group
• generalized CAP-subgroup
• U-embedded subgroup
• solubly saturated formation
• p-nilpotent group
• supersoluble subgroup

Let A be a subgroup of a finite group G. We say that A is a generalized CAP-subgroup of G if for each chief factor H/K of G either A avoids H/K or the following holds: (1) If H/K is non-abelian, then vertical bar H : (A boolean AND H) K vertical bar is a p'-number for every p epsilon pi((A boolean AND H) K/K); (2) If H/K is a p-group, then vertical bar G : N-G(K(A boolean AND H))vertical bar is a p-number. In this paper, we use the generalized CAP-subgroup to characterize the structure of finite groups. Some new characterizations of the hypercyclically embedded subgroups of a finite group are obtained and a series of known results are generalized.

• 出版日期2015-10
• 单位江南大学