Abelian generalized Frobenius complements for p-groups and the Hughes problem
Let G be a finite group, M a complex module for G, N the normal subgroup of G generated by the elements of G that have a nontrivial centralizer in M. The factor group G/N is called a generalized Frobenius complement for G. The structure of G/N is studied in this paper. The main result is: If G is a finite p-group of odd order, and G is either abelian-by-cyclic or of maximal class, then all the generalized Frobenius complements for G are abelian. Applications to the Hughes problem are given.
scientific article; zbMATH DE number 4000195