Regular orbits of quasisimple linear groups II

Melissa Lee

doi:10.1016/j.jalgebra.2021.07.005

Regular orbits of quasisimple linear groups II

Melissa Lee

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

7 Citations (Scopus)

Abstract

Let V be a finite-dimensional vector space over a finite field, and suppose G≤ΓL(V) is a group with a unique subnormal quasisimple subgroup E(G) that is absolutely irreducible on V. A base for G is a set of vectors B⊆V with pointwise stabiliser G_B=1. If G has a base of size 1, we say that it has a regular orbit on V. In this paper we investigate the minimal base size of groups G with E(G)/Z(E(G))≅PSL_n(q) in defining characteristic, with an aim of classifying those with a regular orbit on V.

Original language	English
Pages (from-to)	643-717
Number of pages	75
Journal	Journal of Algebra
Volume	586
DOIs	https://doi.org/10.1016/j.jalgebra.2021.07.005
Publication status	Published - 15 Nov 2021
Externally published	Yes

Keywords

Base size
Groups of Lie type
Representation theory of quasisimple groups

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10.1016/j.jalgebra.2021.07.005

Cite this

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title = "Regular orbits of quasisimple linear groups II",

abstract = "Let V be a finite-dimensional vector space over a finite field, and suppose G≤ΓL(V) is a group with a unique subnormal quasisimple subgroup E(G) that is absolutely irreducible on V. A base for G is a set of vectors B⊆V with pointwise stabiliser GB=1. If G has a base of size 1, we say that it has a regular orbit on V. In this paper we investigate the minimal base size of groups G with E(G)/Z(E(G))≅PSLn(q) in defining characteristic, with an aim of classifying those with a regular orbit on V.",

keywords = "Base size, Groups of Lie type, Representation theory of quasisimple groups",

author = "Melissa Lee",

note = "Funding Information: This paper comprises part of the author's PhD under the supervision of Professor Martin Liebeck. I thank Professor Liebeck for his guidance and careful reading of the paper, the referees for suggesting a number of improvements, and my doctoral examiners Dr. Timothy Burness and Professor David Evans for the corrections they provided to the original version of this work. Financial support from an EPSRC International Doctoral Scholarship at Imperial College London is also gratefully acknowledged. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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doi = "10.1016/j.jalgebra.2021.07.005",

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N1 - Funding Information: This paper comprises part of the author's PhD under the supervision of Professor Martin Liebeck. I thank Professor Liebeck for his guidance and careful reading of the paper, the referees for suggesting a number of improvements, and my doctoral examiners Dr. Timothy Burness and Professor David Evans for the corrections they provided to the original version of this work. Financial support from an EPSRC International Doctoral Scholarship at Imperial College London is also gratefully acknowledged. Publisher Copyright: © 2021 Elsevier Inc.

PY - 2021/11/15

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N2 - Let V be a finite-dimensional vector space over a finite field, and suppose G≤ΓL(V) is a group with a unique subnormal quasisimple subgroup E(G) that is absolutely irreducible on V. A base for G is a set of vectors B⊆V with pointwise stabiliser GB=1. If G has a base of size 1, we say that it has a regular orbit on V. In this paper we investigate the minimal base size of groups G with E(G)/Z(E(G))≅PSLn(q) in defining characteristic, with an aim of classifying those with a regular orbit on V.

AB - Let V be a finite-dimensional vector space over a finite field, and suppose G≤ΓL(V) is a group with a unique subnormal quasisimple subgroup E(G) that is absolutely irreducible on V. A base for G is a set of vectors B⊆V with pointwise stabiliser GB=1. If G has a base of size 1, we say that it has a regular orbit on V. In this paper we investigate the minimal base size of groups G with E(G)/Z(E(G))≅PSLn(q) in defining characteristic, with an aim of classifying those with a regular orbit on V.

KW - Base size

KW - Groups of Lie type

KW - Representation theory of quasisimple groups

UR - https://www.scopus.com/pages/publications/85111232199

U2 - 10.1016/j.jalgebra.2021.07.005

DO - 10.1016/j.jalgebra.2021.07.005

M3 - Article

AN - SCOPUS:85111232199

SN - 0021-8693

VL - 586

SP - 643

EP - 717

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Regular orbits of quasisimple linear groups II

Abstract

Keywords

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