Work

Thompson’s group T is $${3 \over 2}$$-generated

Year: 2025

Type: article

Abstract: Every finite simple group can be generated by two elements and, in fact, every nontrivial element is contained in a generating pair. Groups with this property are said to be $${3 \over 2}$$ 3 2 -generated, and the finite $${3 \over 2}$$ 3 2 -generated groups were recently classified. Turning to infinite groups, in this paper, we prove that the finitely presented simple group T of Thompson is $${3 \over 2}$$ 3 2 -generated. Moreover, we exhibit an element ζ ∈ T such that for any nontrivial α ∈ T , there exists γ ∈ T such that 〈 α , ζ γ 〉 = T .

Source: Israel Journal of Mathematics

DOI: 10.1007/s11856-025-2855-6

Authors: Collin Bleak, Scott Harper, Rachel Skipper

Institutions: University of St Andrews, University of Bristol, Heilbronn Institute for Mathematical Research, The Ohio State University

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: National Science Foundation