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Article

Niemenmaa, Markku ; Rytty, Miikka
On central nilpotency in finite loops with nilpotent inner mapping groups. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 49 (2008), issue 2, pp. 271-277
MSC: 20D10, 20D15, 20D35, 20N05 | MR 2426891 | Zbl 1192.20057
Keywords:
loop; group; connected transversals
Summary:
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.
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