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.
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Dedicated to Hanfried Lenz on the occasion of his 80th birthday
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© 1996 Kluwer Academic Publishers, Boston
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Hachenberger, D. (1996). Groups Admitting a Kantor Family and a Factorized Normal Subgroup. In: Jungnickel, D. (eds) Designs and Finite Geometries. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1395-3_9
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DOI: https://doi.org/10.1007/978-1-4613-1395-3_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8604-2
Online ISBN: 978-1-4613-1395-3
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