The non-coprime k(GV) problem

Abstract Let V be a finite faithful completely reducible FG-module for a finite field F and a finite group G. In various cases explicit linear bounds in | V | are given for the numbers of conjugacy classes k ( G V ) and k ( G ) of the semidirect product GV and of the group G respectively. These results concern the so-called non-coprime k ( G V ) -problem.

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