Displaying similar documents to “On finite commutative IP-loops with elementary abelian inner mapping groups of order p 4 ”

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.

On the structure of finite loop capable nilpotent groups

Miikka Rytty (2010)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either C p k × C p l , k > l ≥ 0 as the Sylow p -subgroup for some odd prime p or the group of quaternions as the Sylow 2 -subgroup may not be loop capable.