A recursive construction of difference families in noncyclic groups

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.
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