# Cyclic factorization numbers of finite groups

## TL;DR

This paper introduces the cyclic factorization number of finite groups, providing explicit computations for key classes using Möbius inversion and subgroup analysis.

## Contribution

It defines the cyclic factorization number and develops methods to compute it for various finite groups, advancing understanding of their subgroup structures.

## Key findings

- Explicit formulas for cyclic factorization numbers in specific finite groups
- Application of Möbius inversion to subgroup lattice analysis
- Enhanced understanding of cyclic subgroup structures in finite groups

## Abstract

In this paper we introduce and study the concept of cyclic factorization number of a finite group G. By using the Mobius inversion formula and other methods involving the cyclic subgroup structure, this is explicitly computed for some important classes of finite groups.