Finite widely  c -supersoluble groups and their mutually permutable products

A. F. Vasil’ev; T. I. Vasil’eva; E. N. Myslovets

doi:10.1134/S0037446616030083

Finite widely c-supersoluble groups and their mutually permutable products

Authors: Vasil’ev A.F.¹, Vasil’eva T.I.², Myslovets E.N.¹
Affiliations:
1. Francisk Skorina Gomel State University
2. Belarusian State University of Transport
Issue: Vol 57, No 3 (2016)
Pages: 476-485
Section: Article
URL: https://journals.rcsi.science/0037-4466/article/view/170468
DOI: https://doi.org/10.1134/S0037446616030083
ID: 170468

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Abstract

A group is c-supersoluble if all its chief factors are isomorphic to simple groups. We introduce the notion of widely c-supersoluble group, which generalizes c-supersolubility. We obtain the properties and find applications of products of mutually permutable subgroups. In particular, we establish the wide c-supersolubility of a finite group that is a product of two mutually permutable c-supersoluble subgroups of coprime indices.