6 papers
Dimension subrings of Lie rings
Vasily Ionin, Roman Mikhailov, Tima Petrov
We show that, unlike the lower central series, the dimension series of a Lie ring need not stabilize when two consecutive terms coincide; in fact, arbitrarily long finite plateaux…
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 Parafree Conjecture for Lie rings and associative algebras
Vasily Ionin, Roman Mikhailov
We construct a finitely generated parafree Lie ring with nonzero second homology and, over every nonzero commutative ring, a finitely generated parafree augmented associative algeb…
Ping-pong for basis-conjugating HNN-extension of free group
Vasily Ionin
We isolate a tractable class of HNN-extensions of a free group, namely, multiple HNN-extensions by basis-conjugating embeddings. For this class, we construct a normal form and esta…
On injectivity of Cohen-Wu homomorphism
Vasily Ionin
We give a new elementary proof of the theorem that a natural map from Milnor's construction to the simplicial group of pure braids is injective. Our approach…
Functorial languages in homological algebra and lower central series
Nikita Golub, Vasily Ionin, Lev Mukoseev
There is a general phenomenon in algebra that numerous functors of homological significance admit characterization as derived limits of elementary functors defined over categories…