A lattice theoretic characterization for the existence of a faithful irreducible representation
type: Item
instance of: scholarly article
title: A lattice theoretic characterization for the existence of a faithful irreducible representation
author: Péter P. Pálfy
published in: International Journal of Group Theory
publication date: 2024-10-11T00:00:00Z
review text: Let \(G\) be a finite group. \textit{S. Palcoux}, in [J. Algebra 505, 279--287 (2018; Zbl 1437.20017)], proved the following result: if \(G\) contains a core-free subgroup H such that the interval \(\mathrm{Int}(H, H^{\ast})\) in the subgroup lattice of \(G\) is Boolean, then \(G\) has a faithful irreducible complex representation.\N\NIn the paper under review, the author proves the converse of the previous statement. So, Palcoux's condition is necessary and sufficient.
reviewed by: Enrico Jabara
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 7925508
zbMATH Keywords: faithful irreducible representation
zbMATH Keywords: subgroup lattice
zbMATH Keywords: Boolean lattice
MaRDI profile type: Publication
DOI: 10.22108/IJGT.2023.138541.1862
description: scientific article; zbMATH DE number 7925508