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.
基金Supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi Autonomous Region (No0249001 )the Graduate lnnovation Foundation of Guangxi Autonomous Region
基金Supported in part by NSFC(Nos.11171353,11271085,11401597)NSF of Guangdong Province of China(No.2015A030313791)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Innovative Team Project of Guangdong Province(China)(No.2014KTSCX196)
