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)

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, Professor 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