The group of inertial automorphisms of an abelian group , arXiv:1403.4193

We study the group IAut(A) generated by inertial automorphisms of an abelian group A, that is automorphisms $\g$ with the property that <X,X\g>/X is finite for each X≤A. Clearly IAut(A) contains the group of finitary automorphisms of A, which is known to be locally finite. In a previous paper we showed that IAut(A) is (locally finite)-by-abelian. Here we have that IAut(A) is abelian-by-(locally finite) in the case A is periodic, while in the general case it is not even (locally nilpotent)-by-(locally finite). However IAut(A) has a normal subgroup $\G$ such that $IAut(A)/\G$ is locally finite and $\G$ acts by means of power automorphisms on its derived subgroup, which is abelian. Moreover we describe into details the structure of IAut(A) in some relevant cases for A. We apply our techniques also to the study of groups whose subnormal subgroups are inert.