On the structure of groups of virtually trivial automorphisms

If G is an arbitrary group, then the group Aut(vt)(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 Aut(vt)(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 Aut(vt)(G) is a finitary linear group.