2002/09/20 by Michael K. Kinyon, Kenneth Kunen, J. D. Phillips
Mathematics · #math.GR #msc:20N05
published as Communications in Algebra 32 (2004), 767-786 · 22 pages
arxiv created 2002/09/20 · arxiv updated 2009/11/30
Let Q be a conjugacy closed loop, and N(Q) its nucleus. Then Z(N(Q)) contains all associators of elements of Q. If in addition Q is diassociative (i.e., an extra loop), then all these associators have order 2. If Q is power-associative and |Q| is finite and relatively prime to 6, then Q is a group. If Q is a finite non-associative extra loop, then 16 | |Q|.