Random generators of given orders and the smallest simple Moufang loop

Details Random generators of given orders and the smallest simple Moufang loop Random generators of given orders and the smallest simple Moufang loop

2007-01-24

arxiv.org/abs/math/0701703v1

Algebra Universalis 50 (2003), 27-33

Mathematics

Group Theory

7 pages

Scientific paper

The probability that $m$ randomly chosen elements of a finite power associative loop $C$ have prescribed orders and generate $C$ is calculated in terms of certain constants related to the action of $Aut(C)$ on the subloop lattice of $C$. As an illustration, all meaningful probabilities of random generation by elements of given orders are found for the smallest nonassociative simple Moufang loop.

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