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On Sharp Permutation Groups whose Point Stabilizers are Certain Frobenius Groups

We investigate non-geometric sharp permutation groups of type {0,k} whose point stabilizers are certain Frobenius groups. We show that if a point stabilizer has a cyclic Frobenius kernel whose order is a power of a prime and Frobenius complement cyclic of prime order, then the point stabilizer is isomorphic to the symmetric group on 3 letters, and there is up to permutation isomorphism, one such permutation group. Further, we determine a significant structural description of non-geometric sharp permutation groups of type {0,k} whose point stabilizers are Frobenius groups with elementary abelian Frobenius kernel K and Frobenius complement L with |L| = |K|-1. As a result of this structural description, it is shown that the smallest non-solvable Frobenius group cannot be a point stabilizer in a non-geometric sharp permutation group of type {0,k}.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc2137593
Date05 1900
CreatorsNorman, Blake Addison
ContributorsBrozovic, Douglas, Conley, Charles, Schmidt, Ralf
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
FormatText
RightsPublic, Norman, Blake Addison, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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