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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

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

IMPACT FACTOR increased in 2015: 1.616
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Rank 18 out of 312 in category Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 3.614
Source Normalized Impact per Paper (SNIP) 2015: 1.901
Impact per Publication (IPP) 2015: 1.302

Mathematical Citation Quotient (MCQ) 2015: 1.53

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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

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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.

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