Displaying similar documents to “On the solvability of commutative loops and their multiplication groups”

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 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 the structure of finite loop capable Abelian groups

Markku Niemenmaa (2007)

Commentationes Mathematicae Universitatis Carolinae

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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 × C p × C p , where k ≥ 2 and p is an odd prime, are not loop capable groups. We also discuss generalizations of this result.