arXiv math/07017032007-01-24math.GR

Random generators of given orders and the smallest simple Moufang loop

Petr Vojtěchovský

备注：: 7 pages
发表信息：: Algebra Universalis 50 (2003), 27-33

英文摘要：

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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