Geodesic
A recursive construction of difference families in noncyclic groups
Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 251-261 Cet article a éte moissonné depuis la source Math-Net.Ru

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Recursive existence theorems are proved for $(v,k,\lambda)$-difference families in noncyclic groups, and it is deduced that there exist families in $G_1\times\dots\times G_\nu$, where $G_i=GF(p_i^{\alpha_i})$, with parameters $v=\prod_{i=1}^\nu p_i^{\alpha_i}$, $\lambda=k-1$ ($\lambda=k$), $k|(p_i^{\alpha_i}-1)$ $((k-1)|(p_i^{\alpha_i}-1))$, and also with $\lambda=\frac{k-1}2$ ($\lambda=\frac k2$), $p_i\ne2$. The existence of known difference families is used to deduce new difference families, that consist in anumber of cases of nonintersecting blocks. The existence theorems for $(v,k,\lambda)$-difference families in $G$ are existence theorems for BIB-designs $(v,k,\lambda)$ having $G$ as a regular group of automorphisms. Bibliography: 17 titles. 
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     title = {A~recursive construction of difference families in noncyclic groups},
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B. T. Rumov. A recursive construction of difference families in noncyclic groups. Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 251-261. http://geodesic.mathdoc.fr/item/SM_1975_27_2_a6/

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