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On loops which have dihedral 2-groups as inner mapping groups

Published online by Cambridge University Press:  17 April 2009

Markku Niemenmaa
Markku Niemenmaa
Affiliation:
Department of MathematicsUniversity of OuluSF-90570 OuluFinland
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Abstract

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In this paper we consider the situation that a group G has a subgroup H which is a dihedral 2-group and with connected transversals A and B in G. We show that G is then solvable and moreover, if G is generated by the set A ∪ B, then H is subnormal in G. We apply these results to loop theory and it follows that if the inner mapping group of a loop Q is a dihedral 2-group then Q is centrally nilpotent.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 1 , August 1995 , pp. 153 - 160
Copyright
Copyright © Australian Mathematical Society 1995

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