On a Theorem of Ledermann and Neumann

authored by

Benjamin Sambale

Abstract

It is easy to see that the number of automorphisms of a finite group of order n cannot exceed (Formula presented.). 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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

American Mathematical Monthly

Volume

127

Pages

827-834

No. of pages

8

ISSN

0002-9890

Publication date

21.10.2020

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.1909.13220 (Access: Open)
https://doi.org/10.1080/00029890.2020.1803625 (Access: Closed)