The Moufang loops of order 64 and 81

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. Key words: Moufang loop, code loop, 2-loop, classification of Moufang loops, GAP.

• Type: Journal
• Year: 2007
• Where: JSC
• Authors: Gábor P. Nagy, Petr Vojtechovský
• Keywords: JSC 2007, Moufang Loop, Nonassociative Moufang, Order 81