Generalized Bhaskar Rao designs and dihedral groups
نویسندگان
چکیده
منابع مشابه
Partial generalized Bhaskar Rao designs over abelian groups
Let G = EA(g) of order g be the abelian group ZPl X ZPl X . .. X ZPl X ... X ZPn X ZPn X ... X ZPII n whereZpi occurs ri times with IT pp the prime decomposition of g. i = 1 It is shown that the necessary conditions A==O(modg) v?:: 3n v == 0 (mod n) A(V n) == 0 (mod 2) v v n 0 (mod 24) if g is even, A ( _ ) = (0 (mod 6) if g is odd, are sufficient for the existence of a PGBRD(v, 3, A, n; EA(g)).
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We show that for each of the groups S3, D4, Q4, Z4 x Z2 and D6 the necessary conditions are sufficient for the existence of a generalized Bhaskar Rao design. That is, we show that: (i) a GBRD (v, 3, λ; S3) exists if and only if λ ≡ O (mod 6 ) and λv(v 1) ≡ O(mod 24); (ii) if G is one of the groups D4, Q4, and Z4 x Z2, a GBRD (v, 3, λ; G) exists if and only if λ ≡ O(mod 8) and λv(v 1) ≡ O(mod 6)...
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We complete the solution of the existence problem for generalized Bhaskar Rao designs of block size 3 over groups of order 12. In particular we prove that if G is a group of order 12 which is cyclic or dicyclic, then a generalized Bhaskar Rao design, GBRD(v, 3, λ = 12t;G) exists for all v ≥ 3 when t is even and for all v ≥ 4 when t is odd.
متن کاملGeneralized Bhaskar Rao designs with two association classes
In previous work generalized Bhaskar Rao designs whose underlying design is a b~lanced incomplete block design have been considered. In the first section of this paper generalized Bhaskar Rao designs (with 2 association classes) whose underlying design is a group divisible design are defin~d. Some methods for the construction of these designs are developed in the second section. It is shown tha...
متن کاملA composition theorem for generalized Bhaskar Rao designs
Let H be a normal subgroup of a finite group G. We show that: If a GBRD(v, k, A.; G IH) exists and a GBRD(k,j, JA.; H) exists then a GBRD(v,j, AJA.; G) exists. We apply this result to show that: i) If k does not exceed the least prime factor of IG I, then a GBRD(k, k, A; G) exists for all A EO (mod IG I); ii) If G is of order IG Ie lor 5 (mod 6) then a GBRD(v, 3, A = t IG I; G), v>3, exists if ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2004
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2004.01.008