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On finite loops whose inner mapping groups are Abelian II

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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If the inner mapping group of a loop is a finite Abelian group, then the loop is centrally nilpotent. We first investigate the structure of those finite Abelian groups which are not isomorphic to inner mapping groups of loops and after this we show that if the inner mapping group of a loop is isomorphic to the direct product of two cyclic groups of the same odd prime power order pn, then our loop is centrally nilpotent of class at most n + 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 487 - 492
Copyright
Copyright © Australian Mathematical Society 2005

References

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