# The existence of some resolvable block designs with divisibility into groups

Research paper by B. T. Rumov

Indexed on: 01 Apr '76Published on: 01 Apr '76Published in: Mathematical Notes

#### Abstract

This paper proves the existence of resolvable block designs with divisibility into groups GD(v; k, m; λ1, λ2) without repeated blocks and with arbitrary parameters such that λ1 = k, (v−1)/(k−1) ≤ λ2 ≤ vk−2 (and also λ1 ≤ k/2, (v−1)/(2(k−1)) ≤ λ2 ≤ vk−2 in case k is even) k ≥ 4 andp=1 (mod k−1), k < p for each prime divisor p of number v. As a corollary, the existence of a resolvable BIB-design (v, k, λ) without repeated blocks is deduced with X = k (and also with λ = k/2 in case of even k) k ⋗$$\sqrt p v = pk^\alpha$$, where a is a natural number if k is a prime power andα=1 if k is a composite number.