Solvability of commutative automorphic loops

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.

v.2: minor revisions suggested by referee

Cited by in corpus (2)

• The structure of automorphic loops
• On identities in centrally nilpotent Moufang loops and centrally nilpotent A-loops