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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

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Volume 15, Issue 6


Metabelian groups that admit triality

Stephen M. Gagola III
Published Online: 2012-11-01 | DOI: https://doi.org/10.1515/jgt-2012-0022


A problem proposed by Grishkov asks if every metabelian triality group has a corresponding Moufang loop which is a group. Here we show that if minimal counter-examples exist, then such triality groups have to be p-groups. In fact, for any prime p, there exists a metabelian p-group that admits triality and has a corresponding Moufang loop that is not a group. Here we also determine how to strengthen the hypothesis of the original problem so that the corresponding Moufang loop is indeed a group.

About the article

Received: 2012-02-24

Revised: 2012-07-08

Published Online: 2012-11-01

Published in Print: 2012-11-01

Citation Information: Journal of Group Theory, Volume 15, Issue 6, Pages 775–783, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2012-0022.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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