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

Authors : Zhencai SHEN, Baoyu ZHANG, Haonan JIANG

Pages : 420-425

Doi:10.15672/hujms.1114323

View : 16 | Download : 5

Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :Let G be a finite group and S be a proper subgroup of G. A group G is called an S-insert ignore into journalissuearticles values(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