On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups

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.

Authors and Affiliations

1. Department of Mathematics, Shanxi University, 030 006, Taiyuan, Shanxi, P.R. China

   Xiuyun Guo

2. Faculty of Science, The Chinese University of Hong Kong, Shatin N.T., Hong Kong, P.R. China (SAR)

   K. P. Shum

Corresponding authors

Correspondence to Xiuyun Guo or K. P. Shum.

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