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Random generators of given orders and the smallest simple Moufang loop

Petr Vojtěchovský
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Abstract

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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Petr Vojtěchovský. 2007-01-24. Random generators of given orders and the smallest simple Moufang loop. https://arxiv.org/abs/math/0701703

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