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Buchsteiner loops: Associators and constructions
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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 has both nilpotency class 3 and an abelian inner mapping group.
World Scientific Pub Co Pte Lt
Title: Buchsteiner loops: Associators and constructions
Description:
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 has both nilpotency class 3 and an abelian inner mapping group.
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