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

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

2007-01-24

arxiv.org/abs/math/0701695v1

Quasigroups and Related Systems 8 (2001), 97-104

Mathematics

Group Theory

8 pages

Scientific paper

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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