- Hacettepe Journal of Mathematics and Statistics
- Vol: 52 Issue: 2
- A constructive approach: From local subgroups to new classes of finite groups
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 : 10 | Download : 2
Publication Date : 2023-03-31
Article Type : Research
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