The k(GV)-problem revisited

Abstract

Abstract 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 .