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.References
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Additional Information
- Alexander Grishkov
- Affiliation: Departamento de Matemática, Universidade de São Paulo, Caixa Postal 66281, São Paulo-SP, 05311-970, Brazil
- Email: grishkov@ime.usp.br
- Michael Kinyon
- Affiliation: Department of Mathematics, University of Denver, 2360 S. Gaylord Street, Denver, Colorado 80208
- MR Author ID: 267243
- ORCID: 0000-0002-5227-8632
- Email: mkinyon@math.du.edu
- Gábor P. Nagy
- Affiliation: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary
- Email: nagyg@math.u-szeged.hu
- Received by editor(s): November 30, 2011
- Received by editor(s) in revised form: September 27, 2012, and October 3, 2012
- Published electronically: May 29, 2014
- Communicated by: Pham Huu Tiep
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 3029-3037
- MSC (2010): Primary 20N05; Secondary 17B99, 20B15
- DOI: https://doi.org/10.1090/S0002-9939-2014-12053-3
- MathSciNet review: 3223359