Groups Admitting a Kantor Family and a Factorized Normal Subgroup

Dirk Hachenberger ()
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Dirk Hachenberger: Institut für Mathematik der Universität Augsburg

A chapter in Designs and Finite Geometries, 1996, pp 135-143 from Springer

Abstract: 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.

Keywords: Generalized Quadrangle; Elation Generalized Quadrangle; Skew Translation Generalized Quadrangle; Kantor Family; 4-Gonal Family; Translation Net; Partial Congruence Partition; Group Coset Geometry (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-1395-3_9

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DOI: 10.1007/978-1-4613-1395-3_9

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