有限群的m-S-可补子群

doi:10.6040/j.issn.1671-9352.0.2020.399

Abstract

Abstract: Let G be a finite group. A subgroup S of G is said to be m-S-permutable in G, if S=〈A,B〉 for some modular subgroup A and S-permutable subgroup B of G. A subgroup H of G is said to be m-S-supplemented in G, if there are an m-S-permutable subgroup S and a subgroup T of G such that G=HT and H∩T≤S≤H. By using the m-S-supplemented subgroups to characterize the structure of finite groups. Some new characterizations of p-nilpotency and supersolubility of finite groups are obtained and generalize some known results.

Key words: finite group, modular subgroup, S-permutable subgroup, m-S-permutable subgroup, m-S-supplemented subgroup

CLC Number:

O152

LIU Xin, WU Zhen-feng, YANG Nan-ying. Finite groups with some m-S-supplemented subgroups[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 8-13.

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Finite groups with some m-S-supplemented subgroups

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