On finite loops whose inner mapping groups have small orders

Markku Niemenmaa

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

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 nilpotent groups

Miikka Rytty (2010)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either $C_{p^{k}} \times C_{p^{l}}$ , $k > l \geq 0$ as the Sylow $p$ -subgroup for some odd prime $p$ or the group of quaternions as the Sylow $2$ -subgroup may not be loop capable.