Finite groups with permutable Hall subgroups

Abstract

Let $\sigma =\{{\sigma }_i|i\in I\}$ be a partition of the set of all primes $\mathbb{P}$ and $G$ a finite group. A set $\mathcal{H}$ of subgroups of $G$ is said to be a \emph{complete Hall $\sigma$-set} of $G$ if every member $\ne 1$ of $\mathcal{H}$ is a Hall ${\sigma }_i$-subgroup of $G$ for some $i\in I$ and $\mathcal{H}$ contains exactly one Hall ${\sigma }_i$-subgroup of $G$ for every $i$ such that ${\sigma }_i\cap \pi (G)\ne \varnothing$. In this paper, we study the structure of $G$ assuming that some subgroups of $G$ permutes with all members of $\mathcal{H}$.

Cited by in corpus (1)

• Nonlocal Modified KdV Equations and Their Soliton Solutions