Rational representations and permutation representations of finite groups

Bartel, A. and Dokchitser, T. (2016) Rational representations and permutation representations of finite groups. Mathematische Annalen, 364(1-2), pp. 539-558. (doi:10.1007/s00208-015-1223-y)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bartel, Dr Alex
Authors: Bartel, A., and Dokchitser, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematische Annalen
Publisher:Springer
ISSN:0025-5831
ISSN (Online):1432-1807
Published Online:10 May 2015
Copyright Holders:Copyright © 2015 Springer-Verlag Berlin Heidelberg
First Published:First published in Mathematische Annalen 364(1-2):539-558
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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