Brauer \(t\)-tuples.
type: Item
instance of: scholarly article
title: Brauer \(t\)-tuples.
zbMATH Open document ID: 1181.20007
author: Adriana Nenciu
published in: Journal of Algebra
publication date: 2009-10-02T00:00:00Z
review text: Two non-isomorphic finite groups form a Brauer pair if their exist a bijection for the conjugacy classes and a bijection for the irreducible characters that preserve all the character values and the power map. Generalizing the definition of a Brauer pair the notion of a Brauer \(t\)-tuple is introduced. It is shown in this paper that Brauer \(t\)-tuples exist for any \(t\geq 2\), i.e., finite groups \(G_1,\dots,G_t\) exist such that \((G_i,G_j)\) is a Brauer pair for all \(1\leq i\neq j\leq t\). In [\textit{B. Eick} and \textit{J. Müller}, J. Algebra 304, No. 1, 286-303 (2006; Zbl 1124.20004)], it has been shown that for \(p\geq 5\) there are Brauer 4-tuples of \(p\)-groups of order \(p^5\). Here it is proved that for any \(t\geq 2\) and any \(p\geq 3\) there are Brauer \(t\)-tuples of \(p\)-groups of order \(p^n\) for \(n\) large enough.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20E45
zbMATH DE Number: 5610484
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: character tables
zbMATH Keywords: Brauer pairs
zbMATH Keywords: conjugacy classes
zbMATH Keywords: representations of finite groups
zbMATH Keywords: complex irreducible characters
zbMATH Keywords: power maps
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.04.019
OpenAlex ID: W1984569907
cites work: Groups of prime power order with derived subgroup of prime order
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cites work: On \(p\)-groups forming Brauer pairs.
cites work: Q4871631
cites work: Character theory of finite groups
cites work: Weak Cayley Tables
cites work: Character tables of \(p\)-groups with derived subgroup of prime order. I.
cites work: Character tables of \(p\)-groups with derived subgroup of prime order. II.
cites work: Character tables of \(p\)-groups with derived subgroup of prime order. III.
DOI: 10.1016/J.JALGEBRA.2009.04.019
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description: scientific article; zbMATH DE number 5610484