The Equalizer Conjecture For The Free Group of Rank Two | Zendy

Alan D. Logan | Zendy

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The Equalizer Conjecture For The Free Group of Rank Two

Author(s) -

Alan D. Logan

Publication year - 2021

Publication title -

the quarterly journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.922

H-Index - 35

eISSN - 1464-3847

pISSN - 0033-5606

DOI - 10.1093/qmath/haab059

Subject(s) - injective function , homomorphism , rank (graph theory) , conjecture , mathematics , combinatorics , equalizer , group (periodic table) , finitely generated abelian group , invertible matrix , free group , discrete mathematics , pure mathematics , physics , computer science , channel (broadcasting) , telecommunications , quantum mechanics

The equalizer of a set of homomorphisms $S: F(a, b)\rightarrow F(\Delta)$ 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 $g, h:F(\Sigma)\rightarrow F(\Delta)$ when the images are inert in, or retracts of, $F(\Delta)$.

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