Abstract

In 1992, Goichot introduced a complete homology theory for arbitrary groups developed by Vogel. In 1998, Triulzi investigated another complete homology theory using the satellite approach invented by Mislin. These developments provide the motivation to find a new invariant ichd G of a group G, which is related to complete homology theories. We investigate its properties and related questions. In particular, using this invariant, we show that Triulzi complete homology is isomorphic to Vogel–Goichot complete homology in many classes of groups. Also we show that hd G = 0 if and only if G is locally finite when G satisfies one of a number of conditions.