The exponent of finite groups
type: Item
instance of: scholarly article
title: The exponent of finite groups
zbMATH Open document ID: 0854.20035
DOI: 10.1007/BF01196161
author: Avinoam Mann
author: Consuelo Martínez
published in: Archiv der Mathematik
publication date: 1997-01-21T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20P05
zbMATH DE Number: 938569
zbMATH Keywords: exponent
zbMATH Keywords: \(m\)-generated finite groups
zbMATH Keywords: probability
MaRDI profile type: Publication
cites work: Residual properties of free groups and probabilistic methods
cites work: On Power Subgroups of Profinite Groups
cites work: SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR GROUPS OF ODD EXPONENT
cites work: Q3362124
description: scientific article; zbMATH DE number 938569