Anchors of irreducible characters (Q514197)

Given a prime number \(p\), every irreducible character \(\chi\) of a finite group \(G\) determines a unique conjugacy class of \(p\)-subgroups of \(G\) called by the authors the \textit{anchors} of \(\chi\). The aim of this paper is to prove some basic properties of the anchors and to investigate the relation to other \(p\)-groups which can be attached to irreducible characters, such as defect groups and vertices (both in the sense of \textit{J. A. Green} [Math. Z. 107, 133--150 (1968; Zbl 0164.34002)] and in the sense of \textit{G. Navarro} [Trans. Am. Math. Soc. 354, No. 7, 2759--2773 (2002; Zbl 0998.20012)]).