On the structure of finite loop capable nilpotent groups

Miikka Rytty

Displaying similar documents to “On the structure of finite loop capable nilpotent groups”

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.

A note on loops of square-free order

Emma Leppälä, Markku Niemenmaa (2013)

Commentationes Mathematicae Universitatis Carolinae

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Let $Q$ be a loop such that $| Q |$ is square-free and the inner mapping group $I (Q)$ is nilpotent. We show that $Q$ is centrally nilpotent of class at most two.

On centrally nilpotent loops

L. V. Safonova, K. K. Shchukin (2000)

Commentationes Mathematicae Universitatis Carolinae

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Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.

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.