4 citations · 11 across the 19 of their papers we have counts for
19 papers
Principal congruence subgroups in the infinite rank case
Vladimir A. Tolstykh
We obtain a number of analogues of the classical results of the 1960s on the general linear groups and special linear groups f…
On the outer automorphism groups of free groups
Vladimir A. Tolstykh
We prove that the outer automorphism group of a free group of countably infinite rank is complete.
Complete outer automorphism groups of free nilpotent groups
Vladimir A. Tolstykh
We prove that the outer automorphism group of an infinitely generated free nilpotent group of class two is complete.
Elementary equivalence of infinite-dimensional classical groups
Vladimir Tolstykh
Let D be a division ring such that the number of conjugacy classes in the multiplicative group D^* is equal to the power of D^*. Suppose that H(V) is the group GL(V) or PGL(V), whe…
On the logical strength of the automorphism groups of free nilpotent groups
Vladimir Tolstykh
Considering a particular case of a problem posed by Saharon Shelah, we prove that the automorphism group of an infinitely generated free nilpotent group N first-order interprets th…
The small index property for free nilpotent groups
Vladimir Tolstykh
Let F be a relatively free algebra of infinite rank. We say that F has the SMALL INDEX PROPERTY if any subgroup of Gamma=Aut(F) of index at most rank(F) contains the pointwise stab…