Jump to ContentJump to Main Navigation

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

12 Issues per year

IMPACT FACTOR increased in 2014: 1.432
Rank 22 out of 310 in category Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 3.585
Source Normalized Impact per Paper (SNIP) 2014: 1.745
Impact per Publication (IPP) 2014: 1.262

Mathematical Citation Quotient (MCQ) 2014: 1.27



Modular analogues of Jordan's theorem for finite linear groups

Michael J. Collins1

1 University College, Oxford OX1 4BH, England. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2008, Issue 624, Pages 143–171, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2008.084, October 2008

Publication History

Published Online:


In 1878, Jordan [C. Jordan, Mémoire sur les equations différentielle linéaire à intégrale algébrique, J. reine angew. Math. 84 (1878), 89–215.] showed that a finite subgroup of GL(n, ℂ) contains an abelian normal subgroup whose index is bounded by a function of n alone. Previously, the author has given precise bounds [M. J. Collins, On Jordan's theorem for complex linear groups, J. Group Th. 10 (2007), 411–423.]. Here, we consider analogues for finite linear groups over algebraically closed fields of positive characteristic ℓ. A larger normal subgroup must be taken, to eliminate unipotent subgroups and groups of Lie type and characteristic ℓ, and we show that generically the bound is similar to that in characteristic 0—being (n + 1)!, or (n + 2)! when ℓ divides n + 2—given by the faithful representations of minimal degree of the symmetric groups. A complete answer for the optimal bounds is given for all degrees n and every characteristic ℓ.

Comments (0)

Please log in or register to comment.