12 citations · 43 across the 23 of their papers we have counts for
28 papers
Finite and nilpotent strongly verbally closed groups
Anton A. Klyachko, Veronika Yu. Miroshnichenko, Alexander Yu. Olshanskii
We show, in particular, that, if a finite group is a retract of any finite group containing as a verbally closed subgroup, then the centre of is a direct factor of .
Subgroups of groups finitely presented in Burnside varieties
Alexander Olshanskii
For all sufficiently large odd integers , the following version of Higman's embedding theorem is proved in the variety of all groups satisfying the identity …
On Kaluzhnin - Krasner's embedding of groups
A. Yu. Olshanskii
In this note, we consider a 'thrifty' version of Kaluzhnin - Krasner's embedding in wreath products and apply it to extensions by finite groups and to metabelian groups.
On identities in the products of group varieties
Nicholas Boatman, Alexander Olshanskii
Let be the variety of groups satisfying the law . It is proved that for every sufficiently large prime , say , the product …
Embedding construction based on amalgamations of group relators
Alexander Yu. Olshanskii
An embedding construction for groups with a length function was introduced by the author earlier. Here we obtain new properties of this embedding, answerin…
Constructions of torsion-free countable, amenable, weakly mixing groups
Rostislav Grigorchuk, Rostyslav Kravchenko, Alexander Olshanskii
In this note, we construct torsion-free countable, amenable, weakly mixing groups, which answer a question of V. Bergelson. Some results related to verbal subgroups and crystallogr…