Exponent and number of generators in a finite group

TL;DR

This paper establishes a precise upper limit on the number of generators needed for a finite group based on the ratio of its order to its exponent, providing new insights into group structure.

Contribution

It introduces a sharp upper bound relating the number of generators to the order and exponent ratio of finite groups, advancing understanding of their algebraic properties.

Findings

Derived a tight upper bound for generators based on order-exponent ratio

Enhanced theoretical understanding of finite group structure

Provides a tool for analyzing group generation complexity

Abstract

We present a sharp upper bound for the number of generators of a finite group in terms of the ratio between the order and the exponent.