Fixed points of Frobenius groups of automorphisms.
Let \(G\) be a finite group admitting a Frobenius group of automorphisms \(FH\) with kernel \(F\) and complement \(H\) such that \(C_G(F)=1\). The main results described in this paper are: (a) \(|G|=|C_G(H)|^{|H|}\); (b) the rank of \(G\) is bounded by a function of \(|H|\) and the rank of \(C_G(H)\); (c) if \(C_G(H)\) is nilpotent then \(G\) is nilpotent; (d) if \(F\) is cyclic, then the exponent of \(G\) is bounded in terms of the exponent of \(C_G(H)\) and \(|FH|\).
scientific article; zbMATH DE number 5998351