I. Protasov

activity

20102021

most citedAlgebraically determined topologies on permutation groups

16 citations · 84 across the 49 of their papers we have counts for

collaborators

Showing 2014 · math.GRShow all

5 papers · 2 filters

math.GR2014★ 8 cited

On the subset Combinatorics of G-spaces

Igor Protasov, Sergii Slobodianiuk

Let $G$ be a group and let $X$ be a transitive $G$ -space. We classify the subsets of $X$ with respect to a translation invariant ideal $J$ in the Boolean algebra of all s…

math.GR2014

Partitions of groups

Igor Protasov, Sergii Slobodianiuk

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

math.GR2014★ 1 cited

A conjecture on partitions of groups

Igor Protasov, Sergii Slobodianiuk

We conjecture that every infinite group $G$ can be partitioned into countably many cells $G = ⋃_{n \in ω} A_{n}$ such that $co v (A_{n} A_{n}^{- 1}) = ∣ G ∣$ for each $n \in ω$ . Here $cov(A)=\min…

math.GR2014★ 4 cited

A note on partitions of groups

Igor Protasov, Sergii Slobodianiuk

Every infinite group $G$ of regular cardinality can be partitioned $G = A_{1} \cup A_{2}$ so that $G \neq = F A_{1}$ , $G \neq = F A_{2}$ for every subset $F \subset G$ of cardinality $∣ F ∣ < ∣ G ∣$ . The fi…

math.GR2014

Partitions of groups into large subsets

Igor Protasov, Sergii Slobodianiuk

Let G be a group and let k be a cardinal. A subset A of G is called left (right) k-large if there exists a subset F of G such that |F| < { and G = FA (G = AF). We say that A is k-l…