Uniquely 2-divisible Bol loops

Abstract

Although any finite Bol loop of odd prime exponent is solvable, we show there exist such Bol loops with trivial center. We also construct finitely generated, infinite, simple Bruck loops of odd prime exponent for sufficiently large primes. This shows that the Burnside problem for Bruck loops has a negative answer.

arXiv comment9 pages; v.2: new results, reformatted for journal submission; v.3; labels on nuclei switched around. V4: same paper, but the referee wanted a different title