Units of group algebras of non-Abelian groups of order 16 and exponent 4 over \(\mathbb F_{2^k}\).
type: Item
instance of: scholarly article
title: Units of group algebras of non-Abelian groups of order 16 and exponent 4 over \(\mathbb F_{2^k}\).
zbMATH Open document ID: 1264.16039
author: Joe Gildea
published in: Results in Mathematics
publication date: 2013-01-10T00:00:00Z
review text: Let \(G=\langle x,y\mid x^4=1,\;y^4=1,\;(xy)^2=1,\;xy^3=x^3y\rangle\) (\(G=\langle x,y\mid x^4=1,\;y^4=1,\;(xy)^2=1,\;y^3xy=x^3\rangle\)), groups of order 16, \(F_{2^k}G\) the group algebra over the Galois-field and \(V\) its group of normalized units. Continuing the research of several papers such as the author's [Int. J. Algebra Comput. 20, No. 5, 721-729 (2010; Zbl 1205.16031)], the paper by \textit{L. Creedon} and \textit{J. Gildea} [Can. Math. Bull. 54, No. 2, 237-243 (2011; Zbl 1242.16033)], the author determines the structure of the group \(V\) as follows: \((C_2^{10k}\rtimes C_4^k)\rtimes(C_2^k\times C_4^k)\) (\(((C_2^{8k}\rtimes C_4^k)\rtimes C_4^k)\rtimes(C_2^k\times C_4^k)\)).
reviewed by: János Kurdics
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 6124389
zbMATH Keywords: group algebras
zbMATH Keywords: characteristic 2
zbMATH Keywords: unit groups
zbMATH Keywords: groups of normalized units
zbMATH Keywords: groups of order 16
zbMATH Keywords: products of cyclic groups
MaRDI profile type: Publication
full work available at URL: s00025-011-0094-0
OpenAlex ID: W2170543013
cites work: Unitary units in modular group algebras of 2-groups
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cites work: UNITARY UNITS OF THE GROUP ALGEBRA 𝔽2kQ8
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cites work: Units in the modular group algebra of a finite Abelian p-group
cites work: Presentations for Unit Groups of Modular Group Algebras of Groups of Order 16
DOI: 10.1007/S00025-011-0094-0
description: scientific article; zbMATH DE number 6124389