Finitary and Artinian-finitary groups

Abstract

AbstractLet M be a module over the ring R. The finitary automorphism group of M over R is and the Artinian-finitary automorphism group of M over R is We continue our study begun in [9] and [12] of the relationship between these two in some ways similar, but actually quite different types of automorphism group. Our study here involves the generalized finitary group $\{{\rm g} \in {\rm Aut}_{\rm R}{\rm M}{:}\,{\rm M}({\rm g} - 1)$ embeds into some finitely generated R-module which does not fit our earlier pattern of generalized finitary groups as described in [8].