The Free Group of Rank 2 is a Limit of Thompson's Group F

Abstract

We show that the free group of rank 2 is a limit of 2-markings of Thompson's group F in the space of all 2-marked groups. More specifically, we find a sequence of generating pairs for F so that as one goes out the sequence, the length of the shortest relation satisfied by the generating pair goes to infinity.

19 pages, 19 figures

References in corpus (4)

• On $k$-free-like groups
• On identities in Thompson's group
• Free limits of Thompson's group $F$
• Limits of Thompson's group F

Cited by in corpus (3)

• Free limits of Thompson's group $F$
• Limits of metabelian groups
• Limit groups with respect to Thompson's group F and other finitely generated groups