%0 Journal Article
%T Constructions of commutative automorphic loops
%A Premysl Jedlicka
%A Michael Kinyon
%A Petr Vojtechovsky
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0810.2114v2