The Equalizer Conjecture for the Free Group of Rank Two

Alan D. Logan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
8 Downloads (Pure)


The equalizer of a set of homomorphisms S:F(a,b)→F(Δ)S:F(a,b)→F(Δ) has rank at most two if S contains an injective map and is not finitely generated otherwise. This proves a strong form of Stallings’ Equalizer Conjecture for the free group of rank two. Results are also obtained for pairs of homomorphisms g,h:F(Σ)→F(Δ)g,h:F(Σ)→F(Δ) when the images are inert in, or retracts of, F(Δ)F(Δ)⁠.
Original languageEnglish
Pages (from-to)777-793
Number of pages17
JournalQuarterly Journal of Mathematics
Issue number2
Early online date30 Dec 2021
Publication statusPublished - Jun 2022

ASJC Scopus subject areas

  • Mathematics(all)


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