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A new approach to the k(GV)-problem

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 University601 University DriveSan Marcos, TX 78666USA e-mail: [email protected]
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Abstract

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This paper is concerned with the well-known and long-standing k(G V)-problem: If the finite group G acts faithfully and irreducibly on the finite GF(p)-module V and p does not divide the order of G, is the number k(GV) of conjugacy classes of the semidirect product GV bounded above by the order of V? Over the past two decades, through the work of numerous people, by using deep character theoretic arguments this question has been answered in the affirmative except for ρ = 5 for which it is still open. In this paper we suggest a new approach to the k(G V)-problem which is independent of most of the previous work on the problem and which is mainly group theoretical. To demonstrate the potential of the new line of attack we use it to solve the k(G V)-problem for solvable G and large ρ.

MSC classification

Secondary: 20C15: Ordinary representations and characters 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 2 , October 2003 , pp. 193 - 220
Copyright
Copyright © Australian Mathematical Society 2003

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