Principal congruence subgroups in the infinite rank case

Abstract

We obtain a number of analogues of the classical results of the 1960s on the general linear groups GLn(Z) and special linear groups SLn(Z) for the automorphism group ?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 ut(A), describe normal generators of the principal congruence subgroups ?A(m) of the group Aut(A), and obtain an analogue of Brenner's ladder relation for the group Aut(A). © 2019 London Mathematical Society