J. Aust. Math. Soc.  79 (2005), 257-276
The $k(GV)$-problem revisited

Thomas Michael Keller
  Department of Mathematics
  Texas State University
  601 University Drive
  San Marcos, TX 78666
  USA
  keller@txstate.edu


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 $k(GV)$ is the number of conjugacy classes of the semidirect product $GV$, then $k(GV)\leq |V|$. 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 $k(GV)$-problem for large p.
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