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.
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 
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/
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     title = {On the structure of finite loop capable {Abelian} groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {217--224},
     year = {2007},
     volume = {48},
     number = {2},
     mrnumber = {2338090},
     zbl = {1174.20345},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2007_48_2_a3/}
}
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