Details
| Original language | English |
|---|---|
| Pages (from-to) | 827-834 |
| Number of pages | 8 |
| Journal | American Mathematical Monthly |
| Volume | 127 |
| Issue number | 9 |
| Publication status | Published - 21 Oct 2020 |
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.
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: American Mathematical Monthly, Vol. 127, No. 9, 21.10.2020, p. 827-834.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On a Theorem of Ledermann and Neumann
AU - Sambale, Benjamin
N1 - Funding Information: The author is supported by the German Research Foundation (SA 2864/1-2 and SA 2864/3-1).
PY - 2020/10/21
Y1 - 2020/10/21
N2 - 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.
AB - 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.
KW - MSC: Primary 20D45
UR - http://www.scopus.com/inward/record.url?scp=85093658805&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1909.13220
DO - 10.48550/arXiv.1909.13220
M3 - Article
AN - SCOPUS:85093658805
VL - 127
SP - 827
EP - 834
JO - American Mathematical Monthly
JF - American Mathematical Monthly
SN - 0002-9890
IS - 9
ER -