The exponent of finite groups
In this note it is proved that the exponent of an \(m\)-generated finite group divides \(n\) as soon as the probability of a random element to have order diving \(n\) is large enough. And ``large enough'' means that such probability is greater or equal than a function, depending on \(m\) and \(n\), and constructed by using the order of the biggest \(m\)-generated finite group of exponent \(n\), whose existence is known by the positive solution to the restricted Burnside problem by E. Zelmanov.
scientific article; zbMATH DE number 938569