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On Connected Transversals to Dihedral Subgroups of Order 2p n

On Connected Transversals to Dihedral Subgroups of Order 2p n Let G be a group with a dihedral subgroup H of order 2p n , where p is an odd prime. We show that if there exist H-connected transversals in G, then G is a solvable group. We apply this result to the loop theory and show that if the inner mapping group of a finite loop Q is dihedral of order 2p n , then Q is a solvable loop. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

On Connected Transversals to Dihedral Subgroups of Order 2p n

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Hong Kong
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s10011-000-0105-2
Publisher site
See Article on Publisher Site

Abstract

Let G be a group with a dihedral subgroup H of order 2p n , where p is an odd prime. We show that if there exist H-connected transversals in G, then G is a solvable group. We apply this result to the loop theory and show that if the inner mapping group of a finite loop Q is dihedral of order 2p n , then Q is a solvable loop.

Journal

Algebra Colloquium – Springer Journals

Published: Jan 1, 2000

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