J. Aust. Math. Soc.  78 (2005), 429-439
Finite p-nilpotent groups with some subgroups c-supplemented

Xiuyun Guo
  Department of Mathematics
  Shanghai University
  Shanghai 200444
  P. R. of China
K. P. Shum
  Faculty of Science
  The Chinese University of Hong Kong
  Shatin, N.T.
  P. R. of China (SAR)

A subgroup $H$ of a finite group $G$ is said to be c-supplemented in $G$ if there exists a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K$ is contained in $\operatorname{core}_G(H)$. In this paper some results for finite p-nilpotent groups are given based on some subgroups of $P$ c-supplemented in $G$, where p is a prime factor of the order of $G$ and $P$ is a Sylow p-subgroup of $G$. We also give some applications of these results.
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