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Subgroup Structure and Representations of Finite and Algebraic Groups

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Abstract

What can one say about maximal subgroups, or, more generally, the subgroup structure of simple, finite, or algebraic groups? In this survey, we will discuss how group representation theory helps us study this classical problem. These results have been applied to various problems, particularly in group theory, number theory, and algebraic geometry.

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Acknowledgments

This survey is based in part on the plenary address given by the author at the Eighth Congress of Vietnamese Mathematicians (Nha Trang, Vietnam, August 10–14, 2013), as well as the lectures given by the author at the Vietnam Institute of Advanced Study in Mathematics (July 2013) and the University of Southern California (March 2014). It is a pleasure to thank the National Science Foundation, the Vietnam Institute of Advanced Study in Mathematics, and the University of Southern California for partial support.

The author is grateful to the referee for careful reading and helpful comments on the paper.

The author gratefully acknowledges the support of the NSF (grant DMS-1201374) and the Simons Foundation Fellowship 305247.

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  1. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    Pham Huu Tiep

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  1. Pham Huu Tiep
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Correspondence to Pham Huu Tiep.

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This author was Plenary speaker at the Vietnam Congress of Mathematicians 2013.

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Tiep, P.H. Subgroup Structure and Representations of Finite and Algebraic Groups. Vietnam J. Math. 43, 501–513 (2015). https://doi.org/10.1007/s10013-015-0127-1

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