On a Theorem of Ledermann and Neumann

It is easy to see that the number of automorphisms of a finite group of order n cannot exceed . Ledermann and Neumann proved conversely that the order of a finite group G can be bounded by a function depending only on the number of automorphisms of G. While their proof is long and complicated, the r...

Full description

Saved in:
Bibliographic Details
Published in:The American mathematical monthly 2020-10, Vol.127 (9), p.827-834
Main Author: Sambale, Benjamin
Format: Article
Language:English
Subjects:
MSC: Primary 20D45
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is easy to see that the number of automorphisms of a finite group of order n cannot exceed . Ledermann and Neumann proved conversely that the order of a finite group G can be bounded by a function depending only on the number of automorphisms of G. While their proof is long and complicated, the result was rediscovered by Nagrebeckiĭ 14 years later. In this article, we give a short and elementary proof of Ledermann-Neumann's theorem based on some of Nagrebeckiĭ's arguments. We also discuss the history of related conjectures.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2020.1803625