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On Automorphism Groups of Divisible Designs

Published online by Cambridge University Press:  20 November 2018

Dieter Jungnickel
Dieter Jungnickel*
Affiliation:
Justus-Liebig-Universität Giessen, Giessen, F.R. Germany
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A (group) divisible design is a tactical configuration for which the v points are split into m classes of n each, such that points have joining number λ (resp. λ2) if and only if they are in the same (resp. in different) classes. We are interested in such designs with a nice automorphism group. We first investigate divisible designs with equally many points and blocks admitting an automorphism group acting regularly on all points and on all blocks, i.e., with a Singer group (Singer [50] obtained the first result in this direction for the finite projective spaces).

As in the case of block designs, one may expect a divisible design with a Singer group to be equivalent to some sort of difference set; as it turns out, one here obtains a generalisation of the relative difference sets of Butson and Elliott [11] and [20].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 2 , 01 April 1982 , pp. 257 - 297
Copyright
Copyright © Canadian Mathematical Society 1982

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