5 papers
An explicit non-elementary matrix over a bivariate Laurent polynomial ring
Vasiliy Ionin, Artem Semidetnov
Let be the fraction field of a discrete valuation ring. We give an explicit matrix in . The pro…
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…
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…
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…
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…