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On finite loops whose inner mapping groups are Abelian

Published online by Cambridge University Press:  17 April 2009

Markku Niemenmaa
Markku Niemenmaa
Affiliation:
Department of Mathematical Sciences, University of Oulu, PL 3000, 90014 Oulu, Finland
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Abstract

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Loops are nonassociative algebras which can be investigated by using their multiplication groups and inner mapping groups If the inner mapping group of a loop is finite and Abelian, then the multiplication group is a solvable group. It is clear that not all finite Abelian groups can occur as inner mapping groups of loops. In this paper we show that certain finite Abelian groups with a special structure are not isomorphic to inner mapping groups of finite loops. We use our results and show how to construct solvable groups which are not isomorphic to multiplication groups of loops.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 477 - 484
Copyright
Copyright © Australian Mathematical Society 2002

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