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arXiv · 0810.2114

Constructions of commutative automorphic loops

Premysl Jedlicka·Michael Kinyon·Petr Vojtechovsky
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Abstract

A loop whose inner mappings are automorphisms is an \emph{automorphic loop} (or \emph{A-loop}). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain central extensions based on trilinear forms, we construct several classes of commutative A-loops of order a power of 2. We initiate the classification of commutative A-loops of small orders and also of order $p^3$, where $p$ is a prime.

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Premysl Jedlicka, Michael Kinyon, Petr Vojtechovsky. 2008-10-13. Constructions of commutative automorphic loops. https://arxiv.org/abs/0810.2114

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