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A SOLVABILITY CRITERION FOR FINITE LOOPS

Part of: Representation theory of groups Other generalizations of groups

Published online by Cambridge University Press:  30 April 2013

EMMA LEPPÄLÄ  and
MARKKU NIEMENMAA
EMMA LEPPÄLÄ*
Affiliation:
Department of Mathematical Sciences, University of Oulu, PL 3000, 90014 Oulu, Finland
MARKKU NIEMENMAA
Affiliation:
Department of Mathematical Sciences, University of Oulu, PL 3000, 90014 Oulu, Finland email markku.niemenmaa@oulu.fi
*
✉emma.leppala@oulu.fi
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Abstract

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We show that a finite loop, whose inner mapping group is the direct product of a dihedral $2$-group and a nonabelian group of order $pq$ ($p$ and $q$ are distinct odd prime numbers), is solvable.

Keywords

inner mapping groupsolvable loopsolvable group

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks 20N05: Loops, quasigroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 1 , February 2014 , pp. 92 - 96
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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