Actions with nilpotent fixed point subgroup
The following results are proved: Theorems A+B+C. Suppose that \(A\) acts coprime on \(G\) (i.e., \((| A|,| G|)=1\)). (A+C) If \(C_G(A)\) normalizes every \(A\)-invariant Sylow subgroup of \(G\), then it also normalizes every maximal \(A\)-invariant subgroup of \(G\) and every \(A\)-invariant irreducible character of \(G\) is fully factorable. (B) If \(C_G(A)\) is nilpotent, then \(G\) is solvable. Note that \(\chi\in\text{Irr}(G)\) if, for every prime \(p\), \(\chi=\alpha_p\alpha_{p'}\), where \(\alpha_p\) and \(\alpha_{p'}\) are \(p\)-special and \(p'\)-special characters of \(G\), respectively.
scientific article; zbMATH DE number 1145740