The Similarity Between Finitary and Artinian-Finitary Groups

摘要

Let M be a module over the commutative ring R. The finitary automorphism group of M over R is ${rm FAut}_RM ={gin{rm Aut}_RM :M(g-1) {rm is} Rhbox{-}{rm Noetherian}}$ and the Artinian-finitary automorphism group of M over R is ${rm F}_1{rm Aut}_RM = {gin{rm Aut}_RM : M(g-1) {rm is} Rhbox{-}{rm Artinian}}.$ We investigate further the surprisingly close relationship between these two types of automorphism groups. Their group theoretic properties seem practically identical.