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Journal of Group Theory

Editor-in-Chief: Wilson, John S.

Managing Editor: Howie, James / Kramer, Linus / Parker, Christopher W.

Editorial Board Member: Abért, Miklós / Borovik, Alexandre V. / Boston, Nigel / Bridson, Martin R. / Caprace, Pierre-Emmanuel / Giovanni, Francesco / Guralnick, Robert / Jaikin Zapirain, Andrei / Kessar, Radha / Khukhro, Evgenii I. / Kochloukova, Dessislava H. / Malle, Gunter / Olshanskii, Alexander / Remy, Bertrand / Robinson, Derek J.S. / Willis, George

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Rational defect groups and 2-rational characters

1Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.

Citation Information: Journal of Group Theory. Volume 14, Issue 3, Pages 401–412, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/jgt.2010.063, December 2010

Publication History

Received:
2010-03-26
Revised:
2010-07-06
Published Online:
2010-12-01

Abstract

Let D be a defect group of a 2-block B of a finite group G. We conjecture that if D is a rational group and D′ ⩽ Z(D), then the values of all χ ∈ Irr(B) lie in a cyclotomic field ℚm, for some odd integer m. We prove the conjecture when G is solvable or |D| = 8. Examples show that the condition D′ ⩽ Z(D) cannot be relaxed.

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