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IMI/Publicaţii/QRS/Ediţii/QRS v.8, n.1 (8), 2001/

The abstract groups (3, 3 | 3, p), their subgroup structure, and their significance for Paige loops

Authors: Vojtĕchovský P.

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 j 3; p). The subgroup structure of (3; 3 j 3; p) depends on the solvability of a certain quadratic congruence, and it is described here in terms of generators.

Vojtĕchovský P.
Department of Mathematics,
Iowa State University,
Ames, IA 50011,
U.S.A.
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