Let 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 embeds into some finitely generated R-module which does not fit our earlier pattern of generalized finitary groups as described in [8].
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