Abstract
We study the structure of a finite groupG admitting a Kantor family (F, F *) of type (s, t) and a nontrivial normal subgroupX which isfactorized byF ∪ F *. The most interesting cases, giving necessary conditions on the structure ofG and the parameterss andt, are those where a further Kantor family is induced inX, or where a partial congruence partition is induced in the factor groupG/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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Communicated by: D. Jungnickel
Dedicated to Hanfried Lenz on the occasion of his 80th birthday
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Hachenberger, D. Groups admitting a Kantor family and a factorized normal subgroup. Des Codes Crypt 8, 135–143 (1996). https://doi.org/10.1007/BF00130573
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DOI: https://doi.org/10.1007/BF00130573