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Alternating units as free factors in the group of units of integral group rings

Part of: Representation theory of groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  14 June 2011

Jairo Z. Gonçalves  and
Paula M. Veloso
Jairo Z. Gonçalves
Affiliation:
Departamento de Matemática, Universidade de São Paulo, Rua do Matão 1010, Butantã 05508-090, São Paulo (SP), Brazil ([email protected])
Paula M. Veloso
Affiliation:
Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, PO Box 702, 30161-970 Belo Horizonte (MG), Brazil ([email protected])
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Abstract

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Let G be a group of odd order that contains a non-central element x whose order is either a prime p ≥ 5 or 3l, with l ≥ 2. Then, in , the group of units of ℤG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that 〈um, vm〉 = 〈um〉 ∗ 〈vm〉 ≌ ℤ ∗ ℤ

Keywords

integral group ringsfree groupsunits

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 20E05: Free nonabelian groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 695 - 709
Copyright
Copyright © Edinburgh Mathematical Society 2011

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