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

V. I. Murashka

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arXiv · 1610.03006

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

V. I. Murashka

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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.

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V. I. Murashka. 2016-10-10. On a generalization of the concept of S-permutable subgroup of a finite group. https://arxiv.org/abs/1610.03006

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