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Remarks on Translation Transversal Designs

  • In this paper the existence of translation transversal designs which is equivalent to the existence of certain particular partitions in finite groups is studied. All considerations are based on the fact that the particular component of such a partition (the component representing the point classes of the corresponding design) is a normal subgroup of the translation group. With regard to groups admitting an (s,k,\(\lambda\))-partiton, on one hand the already known families of such groups are determined without using R. BAER's, 0.H.KEGEL's and M. SUZUKI' s classification of finite groups with partition and on the other hand some new results on the special structure of p - groups are proved. Furthermore, the existence of a series of nonabelian p - groups of odd order which can be represented as translation groups of certain (s,k,1) - translation transversal designs is shown; moreover, the translation groups are normal subgroups of collineation groups acting regularly on the set of flags of the same designs.

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Author:Dirk Hachenberger
URN (permanent link):urn:nbn:de:hbz:386-kluedo-50436
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (206)
Document Type:Report
Language of publication:English
Publication Date:2017/11/07
Year of Publication:1991
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/07
Number of page:24
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)