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The k(GV)-problem revisited

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Thomas Michael Keller
Thomas Michael Keller
Affiliation:
Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666 USA, e-mail: [email protected]
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Abstract

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Suppose that the finite group G acts faithfully and irreducibly on the finite G-module V of characteristic p not dividing |G|. The well-known k(GV)-problem states that in this situation, if k(G V) is the number of conjugacy classes of the semidirect product GV, then k(GV) ≤ |V|. For p—solvable groups, this is equivalent to Brauer's famous k(B)-problem. In 1996, Robinson and Thompson proved the k(GV) problem for large p. This ultimately led to a complete proof of the k(GV)-problem. In this paper, we present a new proof of the k(G V)-problem for large p.

MSC classification

Secondary: 20C15: Ordinary representations and characters 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 2 , October 2005 , pp. 257 - 276
Copyright
Copyright © Australian Mathematical Society 2005

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