Hall-Higman type theorems for exceptional groups of Lie type, I

Pham Huu Tiep; Alexandre E. Zalesski

doi:10.1016/j.jalgebra.2022.01.034

Hall-Higman type theorems for exceptional groups of Lie type, I

Pham Huu Tiep, Alexandre E. Zalesski

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The paper studies the minimum polynomial degrees of p-elements in cross-characteristic representations of simple groups of exceptional Lie type whose BN-pair rank is at most 2. Specifically, we prove that the degree in question equals the order of the element.

Original language	English (US)
Pages (from-to)	755-794
Number of pages	40
Journal	Journal of Algebra
Volume	607
DOIs	https://doi.org/10.1016/j.jalgebra.2022.01.034
State	Published - Oct 1 2022

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Cross-characteristic representations
Finite simple groups of Lie type
Hall-Higman type theorems
Minimum polynomials
p-Elements

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10.1016/j.jalgebra.2022.01.034

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abstract = "The paper studies the minimum polynomial degrees of p-elements in cross-characteristic representations of simple groups of exceptional Lie type whose BN-pair rank is at most 2. Specifically, we prove that the degree in question equals the order of the element.",

keywords = "Cross-characteristic representations, Finite simple groups of Lie type, Hall-Higman type theorems, Minimum polynomials, p-Elements",

author = "Tiep, {Pham Huu} and Zalesski, {Alexandre E.}",

note = "Funding Information: The first author gratefully acknowledges the support of the NSF (grant DMS-1840702), the Joshua Barlaz Chair in Mathematics, and the Charles Simonyi Endowment at the Institute for Advanced Study (Princeton). Publisher Copyright: {\textcopyright} 2022",

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AU - Tiep, Pham Huu

AU - Zalesski, Alexandre E.

N1 - Funding Information: The first author gratefully acknowledges the support of the NSF (grant DMS-1840702), the Joshua Barlaz Chair in Mathematics, and the Charles Simonyi Endowment at the Institute for Advanced Study (Princeton). Publisher Copyright: © 2022

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N2 - The paper studies the minimum polynomial degrees of p-elements in cross-characteristic representations of simple groups of exceptional Lie type whose BN-pair rank is at most 2. Specifically, we prove that the degree in question equals the order of the element.

AB - The paper studies the minimum polynomial degrees of p-elements in cross-characteristic representations of simple groups of exceptional Lie type whose BN-pair rank is at most 2. Specifically, we prove that the degree in question equals the order of the element.

KW - Cross-characteristic representations

KW - Finite simple groups of Lie type

KW - Hall-Higman type theorems

KW - Minimum polynomials

KW - p-Elements

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VL - 607

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EP - 794

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Hall-Higman type theorems for exceptional groups of Lie type, I

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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