Geodesic
On the structure of finite loop capable Abelian groups
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 217-224.

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Loop capable groups are groups which are isomorphic to inner mapping groups of loops. In this paper we show that abelian groups $C_p^{k}\times C_p\times C_p$, where $k\geq 2$ and $p$ is an odd prime, are not loop capable groups. We also discuss generalizations of this result.
Classification : 20D10, 20N05
Keywords: loop; group; connected transversals 
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     title = {On the structure of finite loop capable {Abelian} groups},
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Niemenmaa, Markku. On the structure of finite loop capable Abelian groups. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 217-224. http://geodesic.mathdoc.fr/item/CMUC_2007__48_2_a3/