# Bounding the maximal size of independent generating sets of finite groups

## TL;DR

This paper provides bounds on the maximum size of minimal generating sets of finite groups based on the sum of minimal generators of their Sylow p-subgroups, linking group structure to prime divisors.

## Contribution

It introduces new estimates for m(G) in terms of Sylow p-subgroup generators, connecting group generation properties with prime factorization.

## Key findings

- Derived bounds for m(G) using Sylow p-subgroup generators
- Established relationships between minimal generating sets and prime divisors
- Enhanced understanding of finite group generation complexity

## Abstract

Denote by $m(G)$ the largest size of a minimal generating set of a finite group $G$. We estimate $m(G)$ in terms of $\sum_{p\in \pi(G)}d_p(G),$ where we are denoting by $d_p(G)$ the minimal number of generators of a Sylow $p$-subgroup of $G$ and by $\pi(G)$ the set of prime numbers dividing the order of $G$.