Kyrylo Muliarchyk

activity

20182026

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5 papers · 1 filter

math.GR2026

Failure of direct finiteness for group algebras in every odd characteristic

Elena I. Bunina, Winston Lee, Alexei Miasnikov +1

For every odd prime $p$ , we construct a finitely presented group $G_{p}$ and elements $a, b, c \in F_{p} [G_{p}]$ such that $ab = 1$ , $a c = 0$ , and $c \neq = 0$ . Thus $F_{p} [G_{p}]$ , and…

math.GR2024

Classifying the closure of standard orderings on $Homeo_{+} (R)$

Kyrylo Muliarchyk

We characterize a closure of the set of dynamical-lexicographic orderings on $Homeo_{+} (R)$ and prove the existence of orders outside of it.

math.GR2024

Free products of bi-orderable groups

Kyrylo Muliarchyk

We prove a bi-ordered version of Rivas' result for free products of left-order groups. Namely, we show that a free product of bi-ordered groups does not admit isolated bi-ordering.…

math.GR2021

On the topology of the space of bi-orderings of a free group on two generators

Serhii Dovhyi, Kyrylo Muliarchyk

Let $G$ be a group. We can topologize the spaces of left-orderings $L O (G)$ and bi-orderings $O (G)$ of $G$ with the product topology. These spaces may or may not have isolated point…

math.GR2018

Topology of the space of bi-orderings of a free group on two generators

Kyrylo Muliarchyk, Serhii Dovhyi

Let $G$ be a group. We can topologize the spaces of left-orderings $L O (G)$ and bi-orderings $O (G)$ of $G$ with the product topology. These spaces may or may not have isolated point…

Failure of direct finiteness for group algebras in every odd characteristic

Classifying the closure of standard orderings on Homeo+​(R)

Free products of bi-orderable groups

On the topology of the space of bi-orderings of a free group on two generators

Topology of the space of bi-orderings of a free group on two generators

Classifying the closure of standard orderings on $Homeo_{+} (R)$