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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Finite subgroups of algebraic groups
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by Michael J. Larsen and Richard Pink
J. Amer. Math. Soc. 24 (2011), 1105-1158
Published electronically: April 28, 2011


Generalizing a classical theorem of Jordan to arbitrary characteristic, we prove that every finite subgroup of $\operatorname {GL}_n$ over a field of any characteristic $p$ possesses a subgroup of bounded index which is composed of finite simple groups of Lie type in characteristic $p$, a commutative group of order prime to $p$, and a $p$-group. While this statement can be deduced from the classification of finite simple groups, our proof is self-contained and uses methods only from algebraic geometry and the theory of linear algebraic groups. We believe that our results can serve as a viable substitute for classification in a range of applications in various areas of mathematics.
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Bibliographic Information
  • Michael J. Larsen
  • Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
  • MR Author ID: 293592
  • Email:
  • Richard Pink
  • Affiliation: Department of Mathematics, ETH Zürich, CH - 8092 Zürich, Switzerland
  • MR Author ID: 139765
  • Email:
  • Received by editor(s): August 20, 2010
  • Received by editor(s) in revised form: September 2, 2010, and January 27, 2011
  • Published electronically: April 28, 2011
  • Additional Notes: The first author was partially supported by a Sloan grant and by NSF grants DMS-9727553 and DMS-0800705.
  • © Copyright 2011 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 24 (2011), 1105-1158
  • MSC (2010): Primary 20G40
  • DOI:
  • MathSciNet review: 2813339