Representations of extensions of simple groups

Scott Harper; Martin W. Liebeck

doi:10.1007/s00013-025-02105-1

Representations of extensions of simple groups

Scott Harper^*
, Martin W. Liebeck

^*Corresponding author for this work

Pure Mathematics

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

Abstract

Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group G factors through a projective representation of G, except for some groups of Lie type in characteristic 2; the exact exceptions for G were determined by Kleidman and Liebeck (1989). We generalise this result in two ways. First we consider all low-dimensional projective representations, not just those of minimal dimension. Second we consider all characteristically simple groups, not just simple groups.

Original language	English
Number of pages	11
Journal	Archiv der Mathematik
Volume	Online first
Early online date	8 Mar 2025
DOIs	https://doi.org/10.1007/s00013-025-02105-1
Publication status	E-pub ahead of print - 8 Mar 2025

Keywords

Projective representation
Extensions
Simple group

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Group Generations From Finite to Infinit: Group Generation: From Finite to Infinite
Harper, S. (PI)
EPSRC
1/04/23 → 30/09/25
Project: Fellowship

Cite this

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abstract = "Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group G factors through a projective representation of G, except for some groups of Lie type in characteristic 2; the exact exceptions for G were determined by Kleidman and Liebeck (1989). We generalise this result in two ways. First we consider all low-dimensional projective representations, not just those of minimal dimension. Second we consider all characteristically simple groups, not just simple groups.",

keywords = "Projective representation, Extensions, Simple group",

author = "Scott Harper and Liebeck, \{Martin W.\}",

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AU - Liebeck, Martin W.

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Y1 - 2025/3/8

N2 - Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group G factors through a projective representation of G, except for some groups of Lie type in characteristic 2; the exact exceptions for G were determined by Kleidman and Liebeck (1989). We generalise this result in two ways. First we consider all low-dimensional projective representations, not just those of minimal dimension. Second we consider all characteristically simple groups, not just simple groups.

AB - Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group G factors through a projective representation of G, except for some groups of Lie type in characteristic 2; the exact exceptions for G were determined by Kleidman and Liebeck (1989). We generalise this result in two ways. First we consider all low-dimensional projective representations, not just those of minimal dimension. Second we consider all characteristically simple groups, not just simple groups.

KW - Projective representation

KW - Extensions

KW - Simple group

U2 - 10.1007/s00013-025-02105-1

DO - 10.1007/s00013-025-02105-1

M3 - Article

SN - 0003-889X

VL - Online first

JO - Archiv der Mathematik

JF - Archiv der Mathematik

ER -

Representations of extensions of simple groups

Abstract

Keywords

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Projects

Group Generations From Finite to Infinit: Group Generation: From Finite to Infinite

Cite this