On nilpotent Moufang loops with central associators

2007

Abstract In this paper, we investigate Moufang p-loops of nilpotency class at least three for p > 3 . The smallest examples have order p 5 and satisfy the following properties: (1) They are of maximal nilpotency class, (2) their associators lie in the center, and (3) they can be constructed using a general form of the semidirect product of a cyclic group and a group of maximal class. We present some results concerning loops with these properties. As an application, we classify proper Moufang loops of order p 5 , p > 3 , and collect information on their multiplication groups.

Wielandt's results for algebraic k-groups

2006

We analyze the relation between subnormality and nilpotence, the subnormal joint property, some criteria of subnormality, the norm and the Wielandt subgroup in the case of algebraic groups defined over an arbitrary field.

Cyclic-by-abelian Moufang loops

2010