30 citations · 261 across the 45 of their papers we have counts for
3 papers · 1 filter
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…
Verbally closed virtually free subgroups
Anton A. Klyachko, Andrey M. Mazhuga
A theorem of Myasnikov and Roman'kov says that any verbally closed subgroup of a finitely generated free group is a retract. We prove that all free (and many virtually free) verbal…
Quasiperiodic and mixed commutator factorizations in free products of groups
S. V. Ivanov, Anton A. Klyachko
It is well known that a nontrivial commutator in a free group is never a proper power. We prove a theorem that generalizes this fact and has several worthwhile corollaries. For exa…