Homological properties of abstract and profinite modules and groups

Generalising the main results from [F. Grunewald, A. Jaikin, A. Pinto, P. Zalesskii, Normal subgroups of profinite groups of non-negative deficiency (preprint); D.H. Kochloukova, On a conjecture of E. Rapaport Strasser about knot-like groups and its pro-p version, J. Pure Appl. Algebra 204 (3) (2006) 536-554; D.H. Kochloukova, Some Novikov rings that are von Neumann finite and knot-like groups, Comment. Math. Helv. 81 (4) (2006) 931-943] we study homological finiteness properties and projective dimensions of modules over groups G in the abstract and profinite case comparing with the same invariants for some specific normal subgroups N of G.