2022/10/07 by Gili Golan, Golan, Gili
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2210.03564
openalex publication_date 2022/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recall that a group G is said to be (3)/(2)-generated if every non-trivial element of G belongs to a generating pair of G. Thompson's group V was proved to be (3)/(2)-generated by Donoven and Harper in 2019. It was the first example of an infinite finitely presented non-cyclic (3)/(2)-generated group. Recently, Bleak, Harper and Skipper proved that Thompson's group T is also (3)/(2)-generated. In this paper, we prove that Thompson's group F is "almost" (3)/(2)-generated in the sense that every element of F whose image in the abelianization forms part of a generating pair of ℤ2 is part of a generating pair of F. We also prove that for every non-trivial element f∈ F there is an element g∈ F such that the subgroup ⟨ f,g⟩ contains the derived subgroup of F. Moreover, if f does not belong to the derived subgroup of F, then there is an element g∈ F such that ⟨ f,g⟩ has finite index in F.