• Finite groups all of whose minimal subgroups are $NE^{\ast}$-subgroups

• # Fulltext

Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/124/04/0501-0509

• # Keywords

$NE$-subgroup; $NE^{\ast}$-subgroup; the generalized fitting subgroup; saturated formation.

• # Abstract

Let 𝐺 be a finite group. A subgroup 𝐻 of 𝐺 is called an $NE$-subgroup of 𝐺 if it satisfies $H^G \cap N_{G}(H) = H$. A subgroup 𝐻 of 𝐺 is said to be a $NE^{\ast}$-subgroup of 𝐺 if there exists a subnormal subgroup 𝑇 of 𝐺 such that $G = HT$ and $H \cap T$ is a $NE$-subgroup of 𝐺. In this article, we investigate the structure of 𝐺 under the assumption that subgroups of prime order are $NE^{\ast}$-subgroups of 𝐺. The finite groups, all of whose minimal subgroups of the generalized Fitting subgroup are $NE^{\ast}$-subgroups are classified.

• # Author Affiliations

1. Lijiang College of Guangxi Normal University, Guangxi, Guilin 541006, People’s Republic of China
2. Department of Mathematics, Guangxi Normal University, Guangxi, Guilin 541004, People’s Republic of China

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019

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