On Generalized Finitary Groups

We introduce a wide range of generalized finitary automorphism groups of an arbitrary module M over an arbitrary ring R. The largest such subgroup of AutRM that we seriously consider here is the subgroup of all R-automorphisms g of M such that M(g − 1) has Krull dimension. We also consider the subgroup of all R-automorphisms g of M such that M(g − 1) is Artinian as an R-module. The results are vaguely analogous to the genuine finitary case but are somewhat weaker.