Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus


IMPACT FACTOR 2018: 0.470
5-year IMPACT FACTOR: 0.520

CiteScore 2018: 0.53

SCImago Journal Rank (SJR) 2018: 0.566
Source Normalized Impact per Paper (SNIP) 2018: 1.047

Mathematical Citation Quotient (MCQ) 2018: 0.48

Online
ISSN
1435-4446
See all formats and pricing
More options …
Volume 10, Issue 4

Issues

On Jordan's theorem for complex linear groups

Michael J Collins
Published Online: 2007-07-26 | DOI: https://doi.org/10.1515/JGT.2007.032

Abstract

In 1878, Jordan showed that a finite subgroup of GL(n, ℂ) must possess an abelian normal subgroup whose index is bounded by a function of n alone. We will give the optimal bound for all n; for n ⩾ 71, it is (n + 1)!, afforded by the symmetric group S n+1. We prove a ‘replacement theorem’ that enables us to study linear groups by breaking them down into individual primitive constituents and we give detailed information about the structure of the groups that achieve the optimal bounds, for every degree n.

Our proof relies on known lower bounds for the degrees of faithful representations of each quasisimple group, depending on the classification of finite simple groups, through the use of the bounds for primitive groups that the author has previously obtained.

About the article


Received: 2006-09-08

Published Online: 2007-07-26

Published in Print: 2007-07-20


Citation Information: Journal of Group Theory, Volume 10, Issue 4, Pages 411–423, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/JGT.2007.032.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[2]
V. L. Popov
Mathematical Notes, 2018, Volume 103, Number 5-6, Page 811
[3]
Sylvester Eriksson-Bique
Geometry & Topology, 2018, Volume 22, Number 4, Page 1961
[4]
Ignasi Mundet i Riera and Alexandre Turull
Advances in Mathematics, 2015, Volume 272, Page 820
[5]
Bruno P. Zimmermann
Archiv der Mathematik, 2014, Volume 103, Number 2, Page 195
[6]
Michael J. Collins
Journal of Algebra, 2008, Volume 319, Number 2, Page 759
[7]
Alessandra Guazzi and Bruno Zimmermann
Monatshefte für Mathematik, 2013, Volume 169, Number 3-4, Page 371
[8]
Ivan Cheltsov and Constantin Shramov
Geometry & Topology, 2011, Volume 15, Number 4, Page 1843
[9]
A.S. Detinko, D.L. Flannery, and E.A. OʼBrien
Journal of Algebra, 2011, Volume 344, Number 1, Page 397
[10]
Michael J. Collins
Journal für die reine und angewandte Mathematik (Crelles Journal), 2008, Volume 2008, Number 624

Comments (0)

Please log in or register to comment.
Log in