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On Brauer’s height 0 conjecture

Published online by Cambridge University Press:  22 January 2016

T.R. Berger  and
R. Knörr
T.R. Berger
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
R. Knörr
Affiliation:
Department of Mathematics, University of Essen, 4300 Essen, West, Germany
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R. Brauer not only laid the foundations of modular representation theory of finite groups, he also raised a number of questions and made conjectures (see [1], [2] for instance) which since then have attracted the interest of many people working in the field and continue to guide the research efforts to a good extent. One of these is known as the “Height zero conjecture”. It may be stated as follows:

CONJECTURE. Let B be a p-block of the finite group G. All irreducible ordinary characters of G belonging to B are of height 0 if and only if a defect group of B is abelian.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 109 , March 1988 , pp. 109 - 116
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

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