Geodesic
On central nilpotency in finite loops with nilpotent inner mapping groups
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 271-277
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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.
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.
Classification : 20D10, 20D15, 20D35, 20N05
Keywords: loop; group; connected transversals 
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     title = {On central nilpotency in finite loops with nilpotent inner mapping groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {271--277},
     year = {2008},
     volume = {49},
     number = {2},
     mrnumber = {2426891},
     zbl = {1192.20057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008_49_2_a8/}
}
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Niemenmaa, Markku; Rytty, Miikka. On central nilpotency in finite loops with nilpotent inner mapping groups. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 271-277. http://geodesic.mathdoc.fr/item/CMUC_2008_49_2_a8/