Abstract
Let [Formula: see text] be the fundamental group of a closed [Formula: see text] [Formula: see text]-manifold. We describe the groups [Formula: see text] and [Formula: see text]. We first consider the case where [Formula: see text] is the fundamental group of a torus bundle, and then the case where [Formula: see text] is the fundamental group of a closed [Formula: see text] [Formula: see text]-manifold which is not a torus bundle. The groups are described in terms of some iterated semidirect products of well-known groups, where one exception is for [Formula: see text] for some [Formula: see text], in which case [Formula: see text] is described as an extension and a presentation is given.
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