On a generalization of the concept of S-permutable subgroup of a finite group

TL;DR

This paper generalizes the concept of S-permutable subgroups in finite groups by considering subgroups that permute with certain maximal subgroups associated with a prime partition, revealing lattice structure and deriving known results.

Contribution

It introduces a broader class of subgroups permuting with specific maximal subgroups, establishing their lattice structure and connecting to classical S-permutable subgroup results.

Findings

Such subgroups form a sublattice of the subgroup lattice.

The work generalizes known properties of S-permutable subgroups.

Provides new insights into subgroup permutability in finite groups.

Abstract

Let $\sigma=\{\pi_i | i\in I$ and $\pi_i\cap\pi_j=\emptyset$ for all $i\neq j\}$ be a partition of the set of all primes into mutually disjoint subsets. In this paper we considered subgroups that permutes with given sets of $\pi_i$-maximal subgroups for all $\pi_i\in \sigma$. In particular we showed that such subgroups forms a sublattice of the lattice of all subgroups of a finite group. As corollaries we obtained some well known results about $S$-permutable subgroups.