On finite groups factorised by submodular subgroups

A subgroup \(H\) of a finite group \(G\) is submodular in \(G\) if there is a subgroup chain \(H=H_0\leq\ldots\leq H_i\leq H_{i+1}\leq \ldots \leq H_n=G\) such that \(H_i\) is a modular subgroup of \(H_{i+1}\) for every \(i\). We investigate finite factorised groups with submodular primary (cyclic p...

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Bibliographic Details
Published in:arXiv.org 2023-07
Main Authors: Monakhov, Victor S, Sokhor, Irina L
Format: Article
Language:English
Subjects:
Group theory
Subgroups
Online Access:Get full text
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Summary:A subgroup \(H\) of a finite group \(G\) is submodular in \(G\) if there is a subgroup chain \(H=H_0\leq\ldots\leq H_i\leq H_{i+1}\leq \ldots \leq H_n=G\) such that \(H_i\) is a modular subgroup of \(H_{i+1}\) for every \(i\). We investigate finite factorised groups with submodular primary (cyclic primary) subgroups in factors. We indicate a general approach to the description of finite groups factorised by supersolvable submodular subgroups.
ISSN:2331-8422