  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.
