On the existence of translation nets
- The existence of a translation net of order s and degree r with translation group G is equivalent to the existence of r mutually disjoint subgroups of G of order s. In this paper we consider p-groups G of odd square order p^2n and improve the known general upper bound on the number of mutually disjoint subgroups of order p^n in G provided that G is not elementary abelian. This solves problem 8.2.14 in (D. Jungnickel, Latin Squares, their geometries and their groups. A survey, in "Coding Theory and Design Theory II" (D. K. Ray-Chaudhuri, Ed.), pp. 166-225, Springer, Berlin/New York, 1990.) We determine all groups of order p^4 which are translation groups of translation nets with at least three parallel classes for all prime numbers p. Furthermore, we construct (p^3, p^2 + 1)-translation nets with nonabelian translation group of order p^6 for all odd prime numbers p.
| Author: | Dirk HachenbergerORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-8248 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/968 |
| Parent Title (English): | Journal of Algebra |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 1992 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2008/06/18 |
| Tag: | translation net; translation group; group theory |
| GND-Keyword: | Translationsgruppe; Translation <Mathematik>; Gruppentheorie |
| Volume: | 152 |
| Issue: | 1 |
| First Page: | 207 |
| Last Page: | 229 |
| DOI: | https://doi.org/10.1016/0021-8693(92)90096-5 |
| 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 |
