3 citations · 5 across the 4 of their papers we have counts for
6 papers
On Bergman's property for the automorphism groups of relatively free groups
Vladimir Tolstykh
We say that a group has Bergman's property (the property of universality of finite width) if for every generating set of with we have that for some n…
Infinite-dimensional general linear groups are groups of universally finite width
Vladimir Tolstykh
Recently George Bergman proved that the symmetric group of an infinite set possesses the following property which we call by the {\it universality of finite width}: given any gener…
The palindromic width of a free product of groups
Valery Bardakov, Vladimir Tolstykh
Palindromes are those reduced words of free products of groups that coincide with their reverse words. We prove that a free product of groups has infinite palindromic width, pr…
On the palindromic and primitive widths of a free group
Valery Bardakov, Vladimir Shpilrain, Vladimir Tolstykh
Let G be a group and S a subset of G that generates G. For each x in G define the length l_S(x) of x relative to S to be the minimal k such that x is a product of k elements of S.…
Set theory is interpretable in the automorphism group of a free group
Vladimir Tolstykh
In 1976 S. Shelah posed the following problem: for which variety V of algebras the automorphism group of any free algebra F from V of "large" infinite rank interprets by means of f…
The automorphism tower of a free group
Vladimir Tolstykh
We prove that the automorphism group of an arbitrary non-abelian free group is complete. It generalizes the result by J.Dyer and E.Formanek (1975) stating the completeness of autom…