Character tables of \(p\)-groups with derived subgroup of prime order. I.
type: Item
instance of: scholarly article
title: Character tables of \(p\)-groups with derived subgroup of prime order. I.
zbMATH Open document ID: 1153.20004
author: Adriana Nenciu
published in: Journal of Algebra
publication date: 2008-07-21T00:00:00Z
review text: This paper is the first in a sequence of three papers containing the substance of the author's thesis. Here the following is studied. Two character tables of finite groups are isomorphic if there exist a bijection for the irreducible characters and a bijection for the conjugacy classes that preserve all the character values. Necessary and sufficient conditions for two finite groups are given in order that they have isomorphic character tables. In the case of finite \(p\)-groups with derived subgroup of order \(p\), it is shown that the character tables can be classified by equivalence classes of certain homomorphisms of Abelian \(p\)-groups. In the other papers a purely combinatorial description of the isomorphism classes of character tables of \(p\)-groups \(P\) with \(|[P,P]|=p\) will be provided.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 5303141
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: character tables
zbMATH Keywords: derived subgroups
zbMATH Keywords: algorithms for constructing \(p\)-groups
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.01.020
OpenAlex ID: W2079818929
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DOI: 10.1016/J.JALGEBRA.2008.01.020
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description: scientific article; zbMATH DE number 5303141