Solvability of commutative automorphic loops

Grishkov, Alexander; Kinyon, Michael; Nagy, Gábor

doi:10.1090/S0002-9939-2014-12053-3

Solvability of commutative automorphic loops
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by Alexander Grishkov, Michael Kinyon and Gábor P. Nagy PDF

Proc. Amer. Math. Soc. 142 (2014), 3029-3037 Request permission

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.

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