|
|||||
|
|
On P𝔉-Supplemented subgroups of finite groups |
|
| Authors: | Baojun Li Yuemei Mao Alexander N Skiba |
| Institution: | 1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, P. R. Chinabaojunli@cuit.edu.cn;3. School of Mathematics and Computer Science, University of Datong, Datong, P. R. China;4. Department of Mathematics, Francisk Skorina Gomel State University, Gomel, Belarus |
| Abstract: | Let 𝔉 be a class of groups and G a finite group. A maximal subgroup M of G is called 𝔉-abnormal provided G∕MG?𝔉. Let K<H be subgroup of G. Then we say that (K,H) is an 𝔉-abnormal pair of G provided K is a maximal 𝔉-abnormal subgroup of H. Let A be a subgroup of G. Then we say that A is 𝔉-quasipermutable in G provided A either covers or avoids every 𝔉-abnormal pair of G. In this paper, we consider some applications of 𝔉-quasipermutable subgroups. |
| Keywords: | Finite group 𝔉 -Quasipermutable subgroup p-Nilpotent group Saturated formation P𝔉 -Supplemented subgroup Supersoluble group |