6533b7d0fe1ef96bd125ad44

RESEARCH PRODUCT

On nilpotent Moufang loops with central associators

Gábor P. NagyMaurizio Valsecchi

subject

Discrete mathematicsPure mathematicsSemidirect productAlgebra and Number TheoryLoops of maximal classGroup (mathematics)Moufang loopsMathematics::Rings and AlgebrasLoops of maximal claCyclic groupCenter (group theory)Nilpotent loopsSemidirect product of loopsNilpotent loopNilpotentMathematics::Group TheorySettore MAT/02 - AlgebraOrder (group theory)MultiplicationNilpotent groupMoufang loopMathematics

description

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.

yearjournalcountryeditionlanguage
2007-01-01
http://hdl.handle.net/10447/60432