Pseudo Sylow Numbers

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Benjamin Sambale

External Research Organisations

  • University of Kaiserslautern
View graph of relations

Details

Original languageEnglish
Pages (from-to)60-65
Number of pages6
JournalAmerican Mathematical Monthly
Volume126
Issue number1
Publication statusPublished - 2 Jan 2019
Externally publishedYes

Abstract

One part of Sylow’s famous theorem in group theory states that the number of Sylow p-subgroups of a finite group is always congruent to 1 modulo p. Conversely, Marshall Hall has shown that not every positive integer n≡1(mod p) occurs as the number of Sylow p-subgroups of some finite group. While Hall’s proof relies on deep knowledge of modular representation theory, we show by elementary means that no finite group has exactly 35 Sylow 17-subgroups.

Keywords

    MSC: Primary 20D20

ASJC Scopus subject areas

Cite this

Pseudo Sylow Numbers. / Sambale, Benjamin.
In: American Mathematical Monthly, Vol. 126, No. 1, 02.01.2019, p. 60-65.

Research output: Contribution to journal › Article › Research › peer review

Sambale B. Pseudo Sylow Numbers. American Mathematical Monthly. 2019 Jan 2;126(1):60-65. doi: 10.1080/00029890.2019.1528825
Sambale, Benjamin. / Pseudo Sylow Numbers. In: American Mathematical Monthly. 2019 ; Vol. 126, No. 1. pp. 60-65.
Download
@article{8ab80ada58b746c8af1eb56cb9874f30,
title = "Pseudo Sylow Numbers",
abstract = "One part of Sylow{\textquoteright}s famous theorem in group theory states that the number of Sylow p-subgroups of a finite group is always congruent to 1 modulo p. Conversely, Marshall Hall has shown that not every positive integer n≡1(mod p) occurs as the number of Sylow p-subgroups of some finite group. While Hall{\textquoteright}s proof relies on deep knowledge of modular representation theory, we show by elementary means that no finite group has exactly 35 Sylow 17-subgroups.",
keywords = "MSC: Primary 20D20",
author = "Benjamin Sambale",
note = "Funding information: author is supported by the German Research Foundation (project SA",
year = "2019",
month = jan,
day = "2",
doi = "10.1080/00029890.2019.1528825",
language = "English",
volume = "126",
pages = "60--65",
journal = "American Mathematical Monthly",
issn = "0002-9890",
publisher = "Mathematical Association of America",
number = "1",

}

Download

TY - JOUR

T1 - Pseudo Sylow Numbers

AU - Sambale, Benjamin

N1 - Funding information: author is supported by the German Research Foundation (project SA

PY - 2019/1/2

Y1 - 2019/1/2

N2 - One part of Sylow’s famous theorem in group theory states that the number of Sylow p-subgroups of a finite group is always congruent to 1 modulo p. Conversely, Marshall Hall has shown that not every positive integer n≡1(mod p) occurs as the number of Sylow p-subgroups of some finite group. While Hall’s proof relies on deep knowledge of modular representation theory, we show by elementary means that no finite group has exactly 35 Sylow 17-subgroups.

AB - One part of Sylow’s famous theorem in group theory states that the number of Sylow p-subgroups of a finite group is always congruent to 1 modulo p. Conversely, Marshall Hall has shown that not every positive integer n≡1(mod p) occurs as the number of Sylow p-subgroups of some finite group. While Hall’s proof relies on deep knowledge of modular representation theory, we show by elementary means that no finite group has exactly 35 Sylow 17-subgroups.

KW - MSC: Primary 20D20

UR - http://www.scopus.com/inward/record.url?scp=85060884558&partnerID=8YFLogxK

U2 - 10.1080/00029890.2019.1528825

DO - 10.1080/00029890.2019.1528825

M3 - Article

AN - SCOPUS:85060884558

VL - 126

SP - 60

EP - 65

JO - American Mathematical Monthly

JF - American Mathematical Monthly

SN - 0002-9890

IS - 1

ER -