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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Most Downloaded Articles
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- Verbally closed subgroups of free groups by Myasnikov, Alexei G. and Roman'kov, Vitaly
- Locally graded groups with a Bell condition on infinite subsets by Delizia, Costantino and Tortora, Antonio
- Groups whose Chermak–Delgado lattice is a chain by Brewster, Ben/ Hauck, Peter and Wilcox, Elizabeth
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
- Published Online:
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.