Displaying similar documents to “Inverse property of nonassociative abelian extensions”

On loops that are abelian groups over the nucleus and Buchsteiner loops

Piroska Csörgö (2008)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient and in some cases necessary conditions for the conjugacy closedness of Q / Z ( Q ) provided the commutativity of Q / N . We show that if for some loop Q , Q / N and Inn Q are abelian groups, then Q / Z ( Q ) is a CC loop, consequently Q has nilpotency class at most three. We give additionally some reasonable conditions which imply the nilpotency of the multiplication group of class at most three. We describe the structure of Buchsteiner loops with abelian inner mapping groups.

Schreier loops

Péter T. Nagy, Karl Strambach (2008)

Czechoslovak Mathematical Journal

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We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.