In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there exist subgroups $H_1, H_2, \ldots, H_k$ such that $G = H_1 H_2 \cdots H_k$ and the number of ways to represent any element $g \in G$ as $g = h_1 h_2 \cdots h_k$ ($h_i \in H_i$) does not depend on the choice of $g$. Moreover, a uniform group factorization consisting of cyclic subgroups is called a uniform cyclic group factorization. First, we show that any finite solvable group admits a uniform cyclic group factorization. Second, we show that whether all finite groups admit uniform cyclic group factorizations or not is equivalent to whether all finite simple groups admit uniform group factorizations or not. Lastly, we give some concrete examples of such factorizations.

翻译：本文引入了称为均匀群分解的一类有限群分解方法，作为有限群精确分解的推广。称一个群 $G$ 允许均匀群分解，如果存在子群 $H_1, H_2, \ldots, H_k$ 使得 $G = H_1 H_2 \cdots H_k$，且任意元素 $g \in G$ 表示为 $g = h_1 h_2 \cdots h_k$（$h_i \in H_i$）的方式数目与 $g$ 的选择无关。进一步地，由循环子群构成的均匀群分解称为均匀循环群分解。首先，我们证明任意有限可解群均允许均匀循环群分解。其次，我们证明所有有限群是否允许均匀循环群分解等价于所有有限单群是否允许均匀群分解。最后，我们给出此类分解的一些具体实例。