### On connected transversals to dihedral subgroups

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Author: Myllylä, Kari1
Organizations: 1University of Oulu, Faculty of Science, Department of Mathematical Sciences
Format: ebook
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
Language: English
Published: 2000
Publish Date: 2000-09-04
Description:

# Abstract

Let G be a group with a dihedral subgroup H of order 2x, where x is an odd number. We show that, if there exist H -connected transversals A and B in G, then G is a solvable group. We apply this result to loop theory and we show that, if the inner mapping group I(Q) of a finite loop Q is dihedral of order 2x, then Q is a solvable loop.

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Series: Acta Universitatis Ouluensis. A, Scientiae rerum naturalium
ISSN-E: 1796-220X
ISBN: 951-42-5766-9
ISBN Print: 951-42-5765-0
Issue: 350
Subjects: