On loops whose inner permutations commute

Piroska Csörgö; Tomáš Kepka

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Displaying similar documents to “On loops whose inner permutations commute”

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.

Multiplication groups of quasigroups and loops III.

Tomáš Kepka, A. Jančařík (1997)

Acta Universitatis Carolinae. Mathematica et Physica

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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 commutative IP-loops with elementary abelian inner mapping groups of order $p^{4}$

Markku Niemenmaa (2010)

Commentationes Mathematicae Universitatis Carolinae

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We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^{4}$ are centrally nilpotent of class at most two.

Displaying similar documents to “On loops whose inner permutations commute”

On the structure of finite loop capable Abelian groups

Multiplication groups of quasigroups and loops III.

On abelian inner mapping groups of finite loops

On finite commutative IP-loops with elementary abelian inner mapping groups of order p 4

On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^{4}$