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math.GR2026
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…
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.RA2026
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…