Moufang[S3,2] Cayley Table

Roger Beresford · science forum beginner Joined: 17 May 2005 Posts: 26

A recently updated Wikipedia article, Moufang Loops, states that "the
smallest non-associative Moufang Loop is M[S3,2] with 12 elements". It
is given by u^2=1, u.g=g^-1.u, with g=S3. Can anyone supply a Cayley
table for this loop, starting from the following table for S3?

1 2 3 4 5 6
2 1 6 5 4 3
3 4 5 6 1 2
4 3 2 1 6 5
5 6 1 2 3 4
6 5 4 3 2 1

Thank you.
Roger Beresford.

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