On weakly -supplemented subgroups of finite groups

Abstract

A subgroup H of a group G is said to be weakly $\mathcal{M}$-supplemented in G if there exists a subgroup B of G provided that (1) G = HB, and (2) if $H_1/H_G$ is a maximal subgroup of $H/H_G,$ then $H_{1}B=B{H}_1<G,$ where H_G is the largest normal subgroup of G contained in H. In this paper, we study the influence of weakly $\mathcal{M}$-supplemented subgroups with given order on the structure of finite groups.

Keywords:

• Chief factor
• p-module subgroup
• Sylow subgroup
• weakly $\mathcal{M}$-supplemented subgroup

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D20

Additional information

Funding

This research is supported by NSFC (Grant #11871062), the Natural Science Foundation of Jiangsu Province (Grant #BK20181451), the Postgraduate Innovation Project of Jiangsu Province (KYCX18_2360) and the NSFC-RFBR (Grant #12011530061).