caa a22 4500 477040497 CHVBK 20180405111316.0 cr unu---uuuuu 170330e19960501xx s 000 0 eng 10.1023/A:1018084909072 doi (NATIONALLICENCE)springer-10.1023/A:1018084909072 Hachenberger Dirk Institut für Mathematik der UniversitätAugsburg, Universitätsstra, D-86135, Augsburg aut Groups Admitting a Kantor Family and a Factorized NormalSubgroup [Elektronische Daten] [Dirk Hachenberger] We study the structure of a finite group Gadmitting a Kantor family F,F * of type (s,t)and a nontrivial normal subgroup X which is factorizedby F ∪ F *. The most interestingcases, giving necessary conditions on the structure of Gand the parameters s and t, are thosewhere a further Kantor family is induced in X, orwhere a partial congruence partition is induced in the factorgroup G/X. Most of the known finite generalizedquadrangles can be constructed as coset geometries with respectto a Kantor family. We show that the parameters of a skew translationgeneralized quadrangle necessarily are powers of the same prime. Furthermore, the structure of nonabelian groups admitting aKantor family consisting only of abelian members is considered. Kluwer Academic Publishers, 1996 Generalized Quadrangle nationallicence Elation Generalized Quadrangle nationallicence Skew Translation Generalized Quadrangle nationallicence Kantor Family nationallicence 4-Gonal Family nationallicence Translation Net nationallicence Partial Congruence Partition nationallicence Group Coset Geometry nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 8/1-2(1996-05-01), 135-143 0925-1022 8:1-2<135 1996 8 10623 https://doi.org/10.1023/A:1018084909072 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1018084909072 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hachenberger Dirk Institut für Mathematik der UniversitätAugsburg, Universitätsstra, D-86135, Augsburg aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 8/1-2(1996-05-01), 135-143 0925-1022 8:1-2<135 1996 8 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 477040497 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer