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 groups ${\mathrm{G}\mathrm{L}}_n(\mathbf{Z})$ and special linear groups ${\mathrm{S}\mathrm{L}}_n(\mathbf{Z})$ for the automorphism group ${\mathrm{\Gamma }}_A=\mathrm{A}\mathrm{u}\mathrm{t}(A)$ of an infinitely generated free abelian group $A\mathrm{.}$ In particular, we obtain a description of normal generators of the group $\mathrm{A}\mathrm{u}\mathrm{t}(A),$ classify the maximal normal subgroups of the group $\mathrm{A}\mathrm{u}\mathrm{t}(A),$ describe normal generators of the principal congruence subgroups ${\mathrm{\Gamma }}_{\text{\hspace{0.17em}⁣}A}(m)$ of the group $\mathrm{A}\mathrm{u}\mathrm{t}(A),$ and obtain an analogue of Brenner’s ladder relation for the group $\mathrm{A}\mathrm{u}\mathrm{t}(A)\mathrm{.}$