SOLVABILITY OF COMMUTATIVE AUTOMORPHIC LOOPS

作者：Grishkov Alexander^*; Kinyon Michael; Nagy Gabor P

来源：Proceedings of the American Mathematical Society, 2014, 142(9): 3029-3037.

DOI：10.1090/S0002-9939-2014-12053-3

• Automorphic loops
• Lie algebras of characteristic 2
• primitive groups

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 %26quot;crust of a thin sandwich%26quot; theorem of Zel%26apos;manov and Kostrikin leads to a contradiction.

• 出版日期2014-9