Artem Semidetnov

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20212026

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math.GR2026

An explicit non-elementary matrix over a bivariate Laurent polynomial ring

Vasiliy Ionin, Artem Semidetnov

Let $F$ be the fraction field of a discrete valuation ring. We give an explicit matrix in $SL_{2} (F [X^{\pm 1}, Y^{\pm 1}]) ∖ E_{2} (F [X^{\pm 1}, Y^{\pm 1}])$ . The pro…

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 $r = aabABabABBAbaabABBAb$ and $r^{'} = aabABabABabABBAbaBAb$ , both in the commutator subgroup of the free group on $a$ and $\mathtt…