Geodesic
On the structure of finite loop capable nilpotent groups
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 349-355.

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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 $C_{p^k} \times C_{p^l}$, $k > l \geq 0$ 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.
Classification : 20D10, 20D15, 20F18, 20N05
Keywords: loop; group; connected transversals 
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     title = {On the structure of finite loop capable nilpotent groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {349--355},
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     volume = {51},
     number = {2},
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     zbl = {1211.20021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2010__51_2_a17/}
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Rytty, Miikka. On the structure of finite loop capable nilpotent groups. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 349-355. http://geodesic.mathdoc.fr/item/CMUC_2010__51_2_a17/