Abstract
Let G be a group with a dihedral subgroup H of order 2pn, 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 2pn, then Q is a solvable loop.
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Communicated by A.C. Kim
1991 Mathematics Subject Classification: 20D10, 20N05
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Csörgö, P., Myllylä, K. & Niemenmaa, M. On Connected Transversals to Dihedral Subgroups of Order 2pn. Algebra Colloq. 7, 105–112 (2000). https://doi.org/10.1007/s10011-000-0105-2
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DOI: https://doi.org/10.1007/s10011-000-0105-2