On abelian inner mapping groups of finite loops

Markku Niemenmaa

Displaying similar documents to “On abelian inner mapping groups of finite loops”

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 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.

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.