On a Theorem of Ledermann and Neumann

verfasst von

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

American Mathematical Monthly

Band

127

Seiten

827-834

Anzahl der Seiten

8

ISSN

0002-9890

Publikationsdatum

21.10.2020

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://doi.org/10.48550/arXiv.1909.13220 (Zugang: Offen)
https://doi.org/10.1080/00029890.2020.1803625 (Zugang: Geschlossen)