A constructive approach: From local subgroups to new classes of finite groups

Year 2023, Volume: 52 Issue: 2, 420 - 425, 31.03.2023

Zhencai Shen Baoyu Zhang Haonan Jıang

https://doi.org/10.15672/hujms.1114323

Abstract

Let G be a finite group and S be a proper subgroup of G. A group G is called an S-(S-quasinormal)-group if every local subgroup of G is either an S-quasinormal subgroup or conjugate to a subgroup of S. The main purpose of this construction is to demonstrate a new way of analyzing the structure of a finite group by the properties and the number of conjugacy classes of its local subgroups.

Keywords

local subgroups, simple groups, solvable groups, S-quasinormal subgroups

Supporting Institution

Natural Science Foundation of China

Project Number

No. 12071181

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