Abstract

An (s,k,λ)-translation divisible design (s,k,λ)-TDD) is a (group) divisible design without repeated blocks and with an automorphism group T (translation group) which acts regularly on all points and such that each T-orbit on the blocks is a partition of the point set. We construct a new class of examples of regular (s,k,λ)-TDD's, with non-abelian p-group as translation group. We study the translation group for regular TDD's and for some transversal TDD's. Finally we characterize regular TDD's by balanced incomplete block designs endowed of a suitable automorphism group

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