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Bol Loops of Nilpotence Class Two

Published online by Cambridge University Press:  20 November 2018

Orin Chein  and
Edgar G. Goodaire
Orin Chein
Affiliation:
Temple University, Philadelphia, PA 19122, U.S.A. email: orin@temple.edu
Edgar G. Goodaire
Affiliation:
Memorial University of Newfoundland, St. John's, NF, A1C 5S7 email: edgar@math.mun.ca
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Abstract

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Call a non-Moufang Bol loop minimally non-Moufang if every proper subloop is Moufang and minimally nonassociative if every proper subloop is associative. We prove that these concepts are the same for Bol loops which are nilpotent of class two and in which certain associators square to 1. In the process, we derive many commutator and associator identities which hold in such loops.

Keywords

20N05Bol loopMoufang loopnilpotentcommutatorassociatorminimally nonassociative
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 2 , 01 April 2007 , pp. 296 - 310
Copyright
Copyright © Canadian Mathematical Society 2007

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