Displaying similar documents to “On the structure of finite loop capable Abelian groups”

On abelian inner mapping groups of finite loops

Markku Niemenmaa (2000)

Commentationes Mathematicae Universitatis Carolinae

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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.

On finite loops and their inner mapping groups

Markku Niemenmaa (2004)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider finite loops and discuss the following problem: Which groups are (are not) isomorphic to inner mapping groups of loops? We recall some known results on this problem and as a new result we show that direct products of dihedral 2-groups and nontrivial cyclic groups of odd order are not isomorphic to inner mapping groups of finite loops.

On loops whose inner permutations commute

Piroska Csörgö, Tomáš Kepka (2004)

Commentationes Mathematicae Universitatis Carolinae

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Multiplication groups of (finite) loops with commuting inner permutations are investigated. Special attention is paid to the normal closure of the abelian permutation group.