The Conjugacy Conjecture for Carter Subgroups

Abstract

This paper concerns the problem of determining the nilpotent self-normalizing (Carter) subgroups of a finite group, in relation to the conjecture that they are conjugate, when they exist. We outline the origin of this conjecture and the methods by which it has been studied. For the most substantial contribution, we refer to the recent paper of E.P. Vdovin [27]. As an illustration of the methods, we determine the Carter subgroups of the almost simple groups with socle PSL n (q), in characteristic r 0 ≥ 5.