2021/02/07 by Ігор Протасов, Igor Protasov, Protasov, Igor · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.2102.03790
finitary coarse structure, Cayley graph, selector
openalex publication_date 2021/02/07 · arxiv created 2021/03/23 · arxiv updated 2021/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a group G, FG denotes the set of all non-empty finite subsets of G. We extend the finitary coarse structure of G from G× G to FG× FG and say that a macro-uniform mapping f: FG → FG (resp. f: [G]2 → G) is a finitary selector (resp. 2-selector) of G if f(A)∈ A for each A∈ FG (resp. A ∈ [G]2 ). We prove that a group G admits a finitary selector iff G admits a 2-selector and iff G is a finite extension of an infinite cyclic subgroup or G is countable and locally finite. We use this result to characterize groups admitting linear orders compatible with finitary coarse structures.