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Displaying similar documents to “On centrally nilpotent loops”

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.

On central nilpotency in finite loops with nilpotent inner mapping groups

Markku Niemenmaa, Miikka Rytty (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider finite loops whose inner mapping groups are nilpotent. We first consider the case where the inner mapping group I ( Q ) of a loop Q is the direct product of a dihedral group of order 8 and an abelian group. Our second result deals with the case where Q is a 2 -loop and I ( Q ) is a nilpotent group whose nonabelian Sylow subgroups satisfy a special condition. In both cases it turns out that Q is centrally nilpotent.

Enumeration of nilpotent loops up to isotopy

Lucien Clavier (2012)

Commentationes Mathematicae Universitatis Carolinae

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We modify tools introduced in [Daly D., Vojtěchovský P., Enumeration of nilpotent loops via cohomology, J. Algebra 322 (2009), no. 11, 4080–4098] to count, for any odd prime q , the number of nilpotent loops of order 2 q up to isotopy, instead of isomorphy.