Geodesic
On abelian inner mapping groups of finite loops
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 4, pp. 687-691.

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In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.
Classification : 20D10, 20N05
Keywords: loop; group; connected transversals 
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Niemenmaa, Markku. On abelian inner mapping groups of finite loops. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 4, pp. 687-691. http://geodesic.mathdoc.fr/item/CMUC_2000__41_4_a3/