Finite Bruck loops

Abstract

Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops X X , showing that X X is essentially the direct product of a Bruck loop of odd order with a 2 2 -element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite 2 2 -element Bruck loops are 2 2 -loops, leaving open the question of whether such obstructions actually exist.