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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122599For 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.8 pagesGroup Theory20D30, 20N10The abstract groups (3, 3 | 3, p), their subgroup structure, and their significance for the non-associative finite simple Moufang loopstext