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Groups Admitting a Kantor Family and a Factorized Normal Subgroup

In: Designs and Finite Geometries

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  • Dirk Hachenberger

    (Institut für Mathematik der Universität Augsburg)

Abstract

We study the structure of a finite group G admitting a Kantor family (F,F*) of type (s, t) and a nontrivial normal subgroup X which is factorized by F ∪ F*. The most interesting cases, giving necessary conditions on the structure of G and the parameters s and t, are those where a further Kantor family is induced in X, or where a partial congruence partition is induced in the factor group G/X. Most of the known finite generalized quadrangles can be constructed as coset geometries with respect to a Kantor family. We show that the parameters of a skew translation generalized quadrangle necessarily are powers of the same prime. Furthermore, the structure of nonabelian groups admitting a Kantor family consisting only of abelian members is considered.

Suggested Citation

  • Dirk Hachenberger, 1996. "Groups Admitting a Kantor Family and a Factorized Normal Subgroup," Springer Books, in: Dieter Jungnickel (ed.), Designs and Finite Geometries, pages 135-143, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1395-3_9
    DOI: 10.1007/978-1-4613-1395-3_9
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