Principal congruence subgroups in the infinite rank case

We obtain a number of analogues of the classical results of the 1960s on the general linear groupsGL n ( Z )and special linear groupsSL n ( Z )for the automorphism groupΓ A = Aut ( A )of an infinitely generated free abelian group A . In particular, we obtain a description of normal generators of the group Aut ( A ) , classify the maximal normal subgroups of the group Aut ( A ) , describe normal generators of the principal congruence subgroupsΓA( m )of the group Aut ( A ) , and obtain an analogue of Brenner's ladder relation for the group Aut ( A ) .