Enumeration of nilpotent loops up to isotopy

Lucien Clavier

Displaying similar documents to “Enumeration of nilpotent loops up to isotopy”

On the structure of finite loop capable nilpotent groups

Miikka Rytty (2010)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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 $C_{p^{k}} \times C_{p^{l}}$ , $k > l \geq 0$ 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 centrally nilpotent loops

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

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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

A note on loops of square-free order

Emma Leppälä, Markku Niemenmaa (2013)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.