Anchors of irreducible characters

Abstract

Given a prime number $p$, every irreducible character $\chi$ of a finite group $G$ determines a unique conjugacy class of $p$-subgroups of $G$ which we will call the anchors of $\chi$. This invariant has been considered by L. Barker in the context of finite $p$-solvable groups. Besides proving some basic properties of these anchors, we investigate the relation to other $p$-groups which can be attached to irreducible characters, such as defect groups, vertices in the sense of J. A. Green and vertices in the sense of G. Navarro.