The Moufang loops of order 64 and 81

Authors:
Gábor P. Nagy;Petr Vojtchovský
Affiliations:
Bolyai Institute, University of Szeged, Aradi vertanuk tere 1, 6720 Szeged, Hungary;Department of Mathematics, University of Denver, Denver, CO 80208, USA
Venue:
Journal of Symbolic Computation
Year:
2007

Citing 1
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Abstract

We classify Moufang loops of order 64 and 81 up to isomorphism, using a linear algebraic approach to central loop extensions. In addition to the 267 groups of order 64, there are 4262 nonassociative Moufang loops of order 64. In addition to the 15 groups of order 81, there are 5 nonassociative Moufang loops of order 81, 2 of which are commutative.