4 papers
math.GR2026
On Some More Problems from the Kourovka Notebook
Vasily Ionin, Artem Semidetnov
We give solutions to several problems in combinatorial group theory recorded as open in the literature. Our main source is the Kourovka Notebook, although we also consider question…
math.GR2026
The stable commutator length of a relator is not a one-relator group invariant
Artem Semidetnov
We show that, for the words and , both in the commutator subgroup of the free group on and $\mathtt…
math.AT2025
The operad associated to a crossed simplicial group
Artem Semidetnov
We introduce and study structured enhancement of the notion of a crossed simplicial group, which we call an operadic crossed simplicial group. We show that with each operadic cross…
math.GR2021
On the geometry of free nilpotent groups
Ruslan Magdiev, Artem Semidetnov
In this article, we study geometric properties of nilpotent groups. We find a geometric criterion for the word problem for the finitely generated free nilpotent groups. By geometri…