Solvability of commutative automorphic loops

Details Solvability of commutative automorphic loops Solvability of commutative automorphic loops

2011-11-30

arxiv.org/abs/1111.7138v1

Mathematics

Group Theory

Scientific paper

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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