Generalized Bhaskar Rao designs and dihedral groups

Authors:
R. J. R. Abel;D. Combe;W. D. Palmer
Affiliations:
School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia;School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia;School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia
Venue:
Journal of Combinatorial Theory Series A
Year:
2004

Citing 1
Cited 2

Design theory

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Abstract

We solve the existence problem for generalized Bhaskar Rao designs of block size 3 for an infinite family of non-abelian groups, the dihedral groups Dn, of order 2n. In our main result we show that for n ≥ 1 and v ≥ 3 the following set of conditions is necessary and sufficient for the existence of a GBRD(v, 3, λ Dn): 1. λ ≡ 0 (mod 2n): 2. λ v(v - 1) ≡ 0 (mod 24).