Constructions of commutative automorphic loops

Details Constructions of commutative automorphic loops Constructions of commutative automorphic loops

2008-10-13

arxiv.org/abs/0810.2114v2

Comm. Algebra 38 (2010), no. 9, 3243-3267

Mathematics

Group Theory

v2: final version to appear in Communications in Algebra

Scientific paper

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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