Abstract
Abstract For a solvable group, a theorem of Gaschutz shows that F ( G ) / Φ ( G ) {F(G)/\Phi(G)} is a direct sum of irreducible G-modules and a faithful G / F ( G ) {G/F(G)} -module. If each of these irreducible modules is primitive, we show that every non-vanishing element of G lies in F ( G ) {F(G)} .
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