Describing units of integral group rings up to commensurability

Florian Eisele; Ann Kiefer; Inneke Van Gelder

doi:10.1016/j.jpaa.2014.09.031

Describing units of integral group rings up to commensurability

Florian Eisele, Ann Kiefer, Inneke Van Gelder

Pure Mathematics

Vrije Universiteit Brussel

Research output: Contribution to journal › Article › peer-review

Abstract

We restrict the types of 2 × 2-matrix rings which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to commensurability of the group of units of the integral group ring ZG for all finite groups G that do not have a non-commutative Frobenius complement as a quotient.

Original language	English
Pages (from-to)	2901-2916
Number of pages	16
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2014.09.031
Publication status	Published - 1 Jul 2015

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10.1016/j.jpaa.2014.09.031

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title = "Describing units of integral group rings up to commensurability",

abstract = "We restrict the types of 2 × 2-matrix rings which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to commensurability of the group of units of the integral group ring ZG for all finite groups G that do not have a non-commutative Frobenius complement as a quotient.",

author = "Florian Eisele and Ann Kiefer and {Van Gelder}, Inneke",

note = "Funding Information: The research is supported by the Research Foundation Flanders (FWO – Vlaanderen), partially by FWO project G.0157.12N . Publisher Copyright: {\textcopyright} 2014 Elsevier B.V.",

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AU - Kiefer, Ann

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Describing units of integral group rings up to commensurability

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