Zassenhaus Conjecture for cyclic‐by‐abelian groups

Zassenhaus Conjecture for torsion units states that every augmentation 1 torsion unit of the integral group ring of a finite group G is conjugate to an element of G in the units of the rational group algebra ℚ G. This conjecture has been proved for nilpotent groups, metacyclic groups and some other...

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Published in:Journal of the London Mathematical Society 2013-08, Vol.88 (1), p.65-78
Main Authors: Caicedo, Mauricio, Margolis, Leo, del Río, Ángel
Format: Article
Language:English
Subjects:
Algebra
Augmentation
Conjugates
Group theory
Integrals
Mathematical analysis
Rings (mathematics)
Torsion
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Margolis, Leo
del Río, Ángel
description Zassenhaus Conjecture for torsion units states that every augmentation 1 torsion unit of the integral group ring of a finite group G is conjugate to an element of G in the units of the rational group algebra ℚ G. This conjecture has been proved for nilpotent groups, metacyclic groups and some other families of groups. It has been also proved for some special groups. We prove the conjecture for cyclic‐by‐abelian groups.
doi_str_mv 10.1112/jlms/jdt002
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subjects Algebra
Augmentation
Conjugates
Group theory
Integrals
Mathematical analysis
Rings (mathematics)
Torsion
title Zassenhaus Conjecture for cyclic‐by‐abelian groups
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