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We prove a weak form of the Krull-Schmidt Theorem concerning the behavior of direct-product decompositions of $G$-groups, biuniform abelian $G$-groups, $G$-semidirect products and the $G$-set $Hom(H,A)$. Here $G$ and $A$ are groups and $H$ is a $G$-group. Our main result is the following. Let $P$ be any group. Let $H_1,\ldots,H_n, H_1',\ldots,H_t'$ be $n+t$ biuniform abelian normal subgroups of $P$. Suppose that the products $H_1,\ldots,H_n, H_1',\ldots,H_t'$ are direct, that is, $H_1 \ldots H_n = H_1 \times \ldots \times H_n$ and $H_1'\ldots H_t' =H_1'\times\ldots\times H_t'$. Then the normal subgroups $H_1\times\ldots\timesH_n$ and $H_1'\times\ldots\times H_t'$ of $P$ are $P$-isomorphic if and only if $n = t$ and there exist two permutations $\sigma$ and $\tau$ of $\{1,2,\ldots,n\}$ such that $[H_i]_m = [H'_\sigma(i)]_m$ and $[H_i]_e = [H'_\tau(i)]_e$ for every $i = 1,2,\ldots,n$.