Uniform Cyclic Group Factorizations of Finite Groups. (arXiv:2302.02831v1 [math.GR] CROSS LISTED)

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 …

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