2008/12/02 by Ales Drapal, Michael Kinyon, Drapal, Ales +1
Mathematics · #20N05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20N05
paper · pdf · doi:10.48550/arxiv.0812.0412
22 pages
arxiv created 2008/12/02 · arxiv updated 2009/12/01
Let Q be a Buchsteiner loop. We describe the associator calculus in three variables, and show that |Q| ≥ 32 if Q is not conjugacy closed. We also show that |Q| ≥ 64 if there exists x ∈ Q such that x2 is not in the nucleus of Q. Furthermore, we describe a general construction that yields all proper Buchsteiner loops of order 32. Finally, we produce a Buchsteiner loop of order 128 that is nilpotency class 3 and possesses an abelian inner mapping group.