On the outer automorphism groups of free groups
We prove that the outer automorphism group of a free group of countably infinite rank is complete.
math.GR↗
arXiv subjects
Vladimir A. Tolstykh
Publications and source records attributed to Vladimir A. Tolstykh.
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 $\mathrm{GL}_n(\mathbf Z)$ and special linear groups $\mathrm{SL}_n(\mathbf Z)$ for the automorphism group $Γ_A=\mathrm{Aut}(A)$ of an infinitely generated free abelian group $A.$ In particular, we obtain a description of normal generators of the group $\mathrm{Aut}(A),$ classify the maximal normal subgroups of the group $\mathrm{Aut}(A),$ describe normal generators of the principal congruence subgroups $Γ_{\!A}(m)$ of the group $\mathrm{Aut}(A),$ and obtain an analogue of Brenner's ladder relation for the group $\mathrm{Aut}(A).$
math.GR↗
Complete outer automorphism groups of free nilpotent groups
We prove that the outer automorphism group $\mathrm{Out}(N)$ of an infinitely generated free nilpotent group $N$ of class two is complete.
math.GR↗