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Walking around the Brauer tree

Published online by Cambridge University Press:  09 April 2009

J. A. Green
J. A. Green
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England
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LetG be a finite group, and k a field of finite characteristic p, such that the polynomial x¦G¦ –1 splits completely in k[x]. Let Β be a kG-block which has defect group D which is cylclic of order pd (d ≧ 1). Brauer showed in a famous paper [2] that, in case d = 1, the decomposition matrix of Β is determined by a certain positive integer e which divides p − 1, and a tree Г, a connected acyclic linear graph of e + 1 vertices and e edges. Twenty-five years later Dade ([3]) extended Brauer's theorem to the general case.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 2 , March 1974 , pp. 197 - 213
Copyright
Copyright © Australian Mathematical Society 1974

References

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