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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 16, Issue 1


On 2-Engel groups and Bruck loops

Jonathan D. H. Smith
Published Online: 2013-01-03 | DOI: https://doi.org/10.1515/jgt-2012-0033


A classical construction associates a Bruck loop with a Moufang or Bol loop on which the squaring map is a permutation. The idea of that construction is now extended to a quadratically closed Bol loop or group (where the squaring operation is surjective) that satisfies the 2-Engel condition (for groups: elements commute with their conjugates). The Bruck loop is built on a space of sequences of elements from the original Bol loop. More generally, given a quadratically closed loop with the 2-Engel condition from the join of the varieties of diassociative and (right) Bol loops, a power-associative loop with the right inverse and automorphic inverse properties is constructed in similar fashion.

About the article

Received: 2012-07-05

Revised: 2012-09-03

Published Online: 2013-01-03

Published in Print: 2013-01-01

Citation Information: Journal of Group Theory, Volume 16, Issue 1, Pages 87–106, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2012-0033.

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© 2013 by Walter de Gruyter Berlin Boston.Get Permission

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