7 citations · 9 across the 19 of their papers we have counts for
26 papers
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…
Infinite groups almost all of whose elements are prime powers
S. V. Ivanov
For every prime , we construct an infinite countable group that contains precisely elements which are not th powers.
On rank of the join of two subgroups in a free group
Sergei V. Ivanov
Let be two finitely generated subgroups of a free group, let denote the subgroup generated by , called the join of , and let neither of $H…
Embedding of groups and quadratic equations over groups
Desmond F. Cummins, Sergei V. Ivanov
We prove that, for every integer , a finite or infinite countable group can be embedded into a 2-generated group in such a way that the solvability of quadratic eq…
On joins and intersections of subgroups in free groups
Sergei V. Ivanov
We study graphs of (generalized) joins and intersections of finitely generated subgroups of a free group. We show how to disprove a lemma of Imrich and Müller on these graphs and h…
On a conjecture of Imrich and Müller
Sergei V. Ivanov
A conjecture of Imrich and Müller on rank of the intersection of subgroups of free groups is disproved.