Profinite Groups With Finite Virtual Length

Abstract

In this paper we introduce the notion of finite virtual length for profinite groups (that is, every series has a bounded number of infinite factors) and we prove a Jordan-Hölder type theorem for profinite groups with finite virtual length. More structural results are provided in the pronilpotent and p-adic analytic cases.2010 Mathematics subject classification: primary 20E18; secondary 20E15.