Group nilpotency from a graph point of view
type: Item
instance of: scholarly article
title: Group nilpotency from a graph point of view
author: Valentina Grazian
author: Andrea Lucchini
author: Carmine Monetta
published in: International Journal of Group Theory
publication date: 2024-10-11T00:00:00Z
review text: This paper gives a quite comprehensive survey of the literature regarding the graphs \(\Gamma_{G}\) which can be associated with a group \(G\). In particular, they focus on the problem of understanding whether or not a finite group \(H\) must be nilpotent provided \(\Gamma_{H}\) is isomorphic to \(\Gamma_{G}\) for a finite nilpotent group \(G\).\N\NThe authors bring a new contribution to the issue mentioned above by proving Theorem 5.1: Let \(G\) and \(H\) be finite \(2\)-generated groups with isomorphic generating graphs. If \(G\) is nilpotent and \(H\) is supersoluble, then \(H\) is nilpotent.
reviewed by: Enrico Jabara
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 7925509
zbMATH Keywords: graph isomorphism
zbMATH Keywords: nilpotency, graphs associated with a group
MaRDI profile type: Publication
DOI: 10.22108/IJGT.2023.137059.1834
description: scientific article; zbMATH DE number 7925509