Solvability of commutative automorphic loops
Group Theory
2012-10-01 v2
Abstract
We prove that every finite, commutative automorphic loop is solvable. We also prove that every finite, automorphic 2-loop is solvable. The main idea of the proof is to associate a simple Lie algebra of characteristic 2 to a hypothetical finite simple commutative automorphic loop. The "crust of a thin sandwich" theorem of Zel'manov and Kostrikin leads to a contradiction.
Cite
@article{arxiv.1111.7138,
title = {Solvability of commutative automorphic loops},
author = {Alexandr Grishkov and Michael Kinyon and Gabor Nagy},
journal= {arXiv preprint arXiv:1111.7138},
year = {2012}
}
Comments
v.2: minor revisions suggested by referee