9 citations · 15 across the 3 of their papers we have counts for
5 papers
Free products of groups are strongly verbally closed
Andrey Mazhuga
In a number of recent works, it has been established that many virtually free groups, almost all fundamental groups of surfaces and all groups which are nontrivial free products of…
Virtually free finite-normal-subgroup-free groups are strongly verbally closed
Anton A. Klyachko, Andrey M. Mazhuga, Veronika Yu. Miroshnichenko
Any virtually free group containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing as a v…
Strongly verbally closed groups
Andrey M. Mazhuga
It was recently proven that all free and many virtually free verbally closed subgroups are algebraically closed in any group. We establish sufficient conditions for a group that is…
Balanced factorisations in some algebras
Anton A. Klyachko, Andrey M. Mazhuga, Anastasia N. Ponfilenko
We prove that, in any field of characteristic not two and not three except the five-element field, each element decomposes into a product of four factors whose sum vanishes. We als…
On free decompositions of verbally closed subgroups of free products of finite groups
Andrey Mazhuga
For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.