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|H :(A ∩H)K | is ...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|H :(A ∩H)K | is a p′-number for every p ∈π((A ∩H)K/K);(2) If H/K is a p-group, then |G : NG(K(A ∩H))| 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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11371335 and 11301227)Wu Wen-Tsun Key Laboratory of Mathematics,USTC,Chinese Academy of Sciences,and Chinese Academy of Sciences Visiting Professorship for Senior International Scientists(Grant No.2010T2J12)
文摘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|H :(A ∩H)K | is a p′-number for every p ∈π((A ∩H)K/K);(2) If H/K is a p-group, then |G : NG(K(A ∩H))| 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.
