(1) Department of Mathematics, Shanxi University, 030 006 Taiyuan, Shanxi, P.R. China;(2) Faculty of Science, The Chinese University of Hong Kong, Shatin N.T., Hong Kong, P.R. China (SAR)
Abstract:
A subgroup H of a finite group
G is called c-normal in
G if there exists a normal subgroup
N of G such that
G = HN and $H \cap N \leq H_{G} = {\rm core}_{G}(H)$. In this paper, we investigate the class of groups
of which every maximal subgroup of its Sylow
p-subgroup is c-normal and the
class of groups of which some minimal subgroups of its Sylow
p-subgroup is c-normal for some prime number
p. Some interesting results are obtained and
consequently, many known results related to
p-nilpotent groups and
p-supersolvable groups are generalized.