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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W. / Wilson, John S.

Managing Editor: Khukhro, Evgenii I. / Kramer, Linus

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Volume 14, Issue 3 (May 2011)


Rational defect groups and 2-rational characters

David Gluck
  • Department of Mathematics, Wayne State University, Detroit, MI 48202, U.S.A.
  • Email:
Published Online: 2010-12-01 | DOI: https://doi.org/10.1515/jgt.2010.063


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.

About the article

Received: 2010-03-26

Revised: 2010-07-06

Published Online: 2010-12-01

Published in Print: 2011-05-01

Citation Information: Journal of Group Theory, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt.2010.063. Export Citation

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