On p-Nilpotency of Finite Groups with Some Subgroups c-Supplemented

• 来源期刊: 代数集刊（英文版）
• 关键词: p-nilpotent groups c-supplemented subgroups maximal subgroups
• 年，卷（期）: 2003,（3）
• 页码范围: 259-266
• 页数: 8页
• 语种: 英文

摘要

A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup K of G such that G = HK and H∩K is contained in coreG(H).In this paper we prove that a group G is p-nilpotent if every maximal subgroup of P is c-supplemented in G and (|G|, p - 1) = 1, where p is a prime factor of the order of G and P is a Sylow p-subgroup of We also give a condition for a group to be p-nilpotent by using the 2-maximal subgroups of the Sylow p-subgroups.