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arXiv · 1509.05700

The Moufang loops of order 64 and 81

Gábor P. Nagy·Petr Vojtěchovský
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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.

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Gábor P. Nagy, Petr Vojtěchovský. 2015-09-18. The Moufang loops of order 64 and 81. https://arxiv.org/abs/1509.05700

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