The structure of automorphic loops (Q2822724)

This paper is a foundation to the structure theory of (non-commutative) automorphic loops. The authors manage to prove several properties that were already known in the commutative case, especially they consider uniquely 2-divisible loops. They use an approach used for Moufang loops and for commutative automorphic loops to associate a Bruck loop with every automorphic loop. Using this Bruck loop, the authors were able to obtain Lagrange and Cauchy theorems for automorphic loops of odd orders.NEWLINENEWLINEAnother approach that works best in the odd case was to construct automorphic loops from Lie rings. This was one of the key ingredients to prove the odd order theorem for commutative automorphic loops.NEWLINENEWLINEThere are a few other results too, e.g. the authors study how a possible finite simple automorphic loop can look like or the authors present a semidirect extension of middle nuclei that yields constructions similar to dihedral groups.