Commutative Moufang Loops

Abstract

Bol [66] was the first to construct a commutative Moufang loop which is not an abelian group. Each of Bol’s examples is centrally nil-potent of class 2. Bruck [70] showed how to construct examples which are centrally nilpotent of class 3. In his University of Wisconsin thesis (1953), T. Slaby formulated the following theorem: Every commutative Moufang loop which can be generated by n elements (n > 1) is centrally nilpotent of class at most n — 1. In collaboration with the author, Slaby proved this theorem for n = 4, 5 as well as for the previously known cases n = 2, 3.