Semiregularity and connectivity of the non-𝔉 graph of a finite group
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Published:2022-06-10
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Volume:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Lucchini Andrea1ORCID,
Nemmi Daniele1
Affiliation:
1. Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Via Trieste 63, 35121 Padova, Italy
Abstract
Given a class [Formula: see text] of finite groups, we consider the graph [Formula: see text] whose vertices are the elements of [Formula: see text] and where two vertices [Formula: see text] are adjacent if and only if [Formula: see text]. Moreover, we denote by [Formula: see text] the set of the isolated vertices of [Formula: see text] and by [Formula: see text] the graph obtained from [Formula: see text] by deleting the isolated vertices. We address the following question: to what extent the fact that [Formula: see text] is a subgroup of [Formula: see text] for any [Formula: see text] implies that the graph [Formula: see text] is connected?
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory