Groups admitting a Kantor family and a factorized normal subgroup
- 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 U 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.
| Author: | Dirk HachenbergerORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-8568 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1000 |
| Parent Title (English): | Designs, Codes and Cryptography |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 1996 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2008/06/19 |
| Tag: | Generalized Quadrangle; Elation Generalized Quadrangle; Skew Translation Generalized Quadrangle; Kantor Family; 4-Gond Family; Translation Net |
| GND-Keyword: | Verallgemeinertes Viereck; Translation <Mathematik>; Gruppentheorie; Restklasse; Projektive Geometrie |
| Volume: | 8 |
| Issue: | 1/2 |
| First Page: | 135 |
| Last Page: | 143 |
| DOI: | https://doi.org/10.1007/BF00130573 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Diskrete Mathematik, Optimierung und Operations Research | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
