On the structure of groups of virtually trivial automorphisms

Abstract

ABSTRACTIf G is an arbitrary group, then the group Autvt(G) consists, by definition, of all virtually trivial automorphisms of G, i.e. of all automorphisms that have the fixed-point subgroup of finite index in G. We investigate the structure of Autvt(G) and show that it possesses a certain “well-behaved” normal series which demonstrates its closeness to finitary linear groups. This is then used to prove that each simple section of Autvt(G) is a finitary linear group.