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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Burness, T.C.


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1435-4446
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Volume 20, Issue 2

Issues

Subgroup Isomorphism Problem for units of integral group rings

Leo Margolis
Published Online: 2016-06-11 | DOI: https://doi.org/10.1515/jgth-2016-0026

Abstract

The Subgroup Isomorphism Problem for Integral Group Rings asks for which finite groups U it is true that if U is isomorphic to a subgroup of V(G), the group of normalized units of the integral group ring of the finite group G, it must be isomorphic to a subgroup of G. The smallest groups known not to satisfy this property are the counterexamples to the Isomorphism Problem constructed by M. Hertweck. However, the only groups known to satisfy it are cyclic groups of prime power order and elementary-abelian p-groups of rank 2. We give a positive solution to the Subgroup Isomorphism Problem for C4×C2. Moreover, we prove that if the Sylow 2-subgroup of G is a dihedral group, any 2-subgroup of V(G) is isomorphic to a subgroup of G.

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About the article


Received: 2015-12-20

Revised: 2016-05-13

Published Online: 2016-06-11

Published in Print: 2017-03-01


Funding Source: DFG

Award identifier / Grant number: Sonderforschungsbereich 701

This research was partly supported by the Sonderforschungsbereich 701 at the University of Bielefeld.


Citation Information: Journal of Group Theory, Volume 20, Issue 2, Pages 289–307, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2016-0026.

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