Over the ring of integers, groups of type Φ were first introduced by Olympia Talelli as a possible algebraic characterisation of groups that admit finite dimensional models for classifying spaces for proper actions. In this short article, we make the same definition over arbitrary commutative rings of finite global dimension and prove a number of properties pertaining to cohomological invariants of these groups with the extra condition that the groups belong to a large hierarchy of groups introduced by Peter Kropholler in the nineties. We prove most of Talelli's conjecture of equivalent statements for type Φ groups for these groups, and expand the scope of a few existing results in the literature.
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