Rational representations and permutation representations of finite groups

Alex Bartel; Tim Dokchitser

doi:10.1007/s00208-015-1223-y

Rational representations and permutation representations of finite groups

Alex Bartel, Tim Dokchitser

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

302 Downloads (Pure)

Abstract

We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we give a solution in that case. As one of the applications, we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large.

Original language	English
Pages (from-to)	539-558
Number of pages	20
Journal	Mathematische Annalen
Volume	364
Issue number	1
Early online date	10 May 2015
DOIs	https://doi.org/10.1007/s00208-015-1223-y
Publication status	Published - Feb 2016

Bibliographical note

16 pages; minor improvements and corrections. To appear in Math. Ann

Keywords

math.RT
math.GR
20C15, 20C33, 19A22

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10.1007/s00208-015-1223-y

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Springer at http://link.springer.com/article/10.1007%2Fs00208-015-1223-y Please refer to any applicable terms of use of the publisher.
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Professor Tim Dokchitser
- Tim.Dokchitserbristol.acuk
- School of Mathematics - Heilbronn Chair in Algebraic/Arithmetic Geometry
- Pure Mathematics
- Number theory and combinatorics
Person: Academic , Member

Cite this

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title = "Rational representations and permutation representations of finite groups",

abstract = "We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we give a solution in that case. As one of the applications, we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large.",

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AU - Dokchitser, Tim

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N2 - We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we give a solution in that case. As one of the applications, we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large.

AB - We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we give a solution in that case. As one of the applications, we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large.

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KW - math.GR

KW - 20C15, 20C33, 19A22

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M3 - Article (Academic Journal)

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EP - 558

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1

ER -

Rational representations and permutation representations of finite groups

Abstract

Bibliographical note

Keywords

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Professor Tim Dokchitser

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