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On the characters of Sylow $ p$-subgroups of finite Chevalley groups $ G(p^f)$ for arbitrary primes

Authors: Tung Le, Kay Magaard and Alessandro Paolini
Journal: Math. Comp. 89 (2020), 1501-1524
MSC (2010): Primary 20C33, 20C15; Secondary 20C40, 20G41
Published electronically: November 19, 2019
MathSciNet review: 3334053
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Abstract: In this work we develop a method to parametrize the set $ \mathrm {Irr}(U)$ of irreducible characters of a Sylow $ p$-subgroup $ U$ of a finite Chevalley group $ G(p^f)$ which is valid for arbitrary primes $ p$, in particular, when $ p$ is a very bad prime for $ G$. As an application, we parametrize $ \mathrm {Irr}(U)$ when $ G=\mathrm {F}_4(2^f)$.

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Additional Information

Tung Le
Affiliation: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Kay Magaard
Affiliation: Department of Mathematics, University of Arizona, 617 Santa Rita Road, Tuscon, Arizona 85721

Alessandro Paolini
Affiliation: FB Mathematik, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany

Keywords: Irreducible character, Sylow subgroup, nonabelian core, arbitrary primes
Received by editor(s): January 31, 2019
Received by editor(s) in revised form: July 29, 2019
Published electronically: November 19, 2019
Additional Notes: Part of this work has been developed during visits: of the second author at the University of Pretoria and at the University of KwaZulu-Natal in June 2018, supported by CoE-Mass FA2018/RT18ALG/007; of the second author in June 2018 and of the first author in January 2019 at the Technische Universität Kaiserslautern, supported by the SFB-TRR 195 “Symbolic Tools in Mathematics and their Application” of the German Research Foundation (DFG) and NRF Incentive Grant 109304; and of the third author in September and October 2018 at the Hausdorff Institute of Mathematics in Bonn during the semester “Logic and Algorithms in Group Theory”, supported by a HIM Research Fellowship
The third author acknowledges financial support from the SFB-TRR 195
Article copyright: © Copyright 2019 American Mathematical Society