On finite loops and their inner mapping groups

Markku Niemenmaa

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Displaying similar documents to “On finite loops and their inner mapping 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 whose inner mapping groups have small orders

Markku Niemenmaa (1996)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.

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 $C_{p}^{k} \times C_{p} \times C_{p}$ , where $k \geq 2$ and $p$ is an odd prime, are not loop capable groups. We also discuss generalizations of this result.