Finitary automorphism groups over commutative rings

We introduce a theory of finitary automorphism groups of arbitrary modules over arbitrary commutative rings, encompassing the theory of finitary linear groups (the field and vector space case). In particular, we have extended the structure theorems of U. Meierfrankenfeld et al. (J. London Math. Soc. 47 (1993 ) 31–40) for locally soluble finitary groups and unipotent finitary groups from the field to the commutative ring case.