Nuclei and Lifts of π-Partial Characters

Abstract

In this paper, we obtain a common generalization of the Isaacs and Navarro constructions of nuclei for characters of π-separable groups. The construction of Isaacs used the lattice of all subnormal subgroups, and the construction of Navarro used the lattice of all normal subgroups. We show that a generalized nucleus can be constructed using other lattices of subnormal subgroups, and these nuclei have properties similar to the properties of the nuclei constructed by Isaacs and Navarro.