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The abstract groups (3, 3 | 3, p), their subgroup structure, and their significance for the non-associative finite simple Moufang loops

Petr Vojtěchovský
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Abstract

For most (and possibly all) non-associative finite simple Moufang loops, three generators of order 3 can be chosen so that each two of them generate a group isomorphic to $(3, 3 | 3, p)$. The subgroup structure of $(3, 3 | 3, p)$ depends on the solvability of a certain quadratic congruence, and it is described here in terms of generators.

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Petr Vojtěchovský. 2007-01-24. The abstract groups (3, 3 | 3, p), their subgroup structure, and their significance for the non-associative finite simple Moufang loops. https://arxiv.org/abs/math/0701695

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