A question of B. Plotkin about the semigroup of endomorphisms of a free group

Formanek, Edward

doi:10.1090/S0002-9939-01-06155-X

A question of B. Plotkin about the semigroup of endomorphisms of a free group
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Proc. Amer. Math. Soc. 130 (2002), 935-937 Request permission

Abstract:

Let $F$ be a free group of finite rank $n \geq 2$, let $End(F)$ be the semigroup of endomorphisms of $F$, and let $Aut(F)$ be the group of automorphisms of $F$. Theorem. If $T : End(F) \to End(F)$ is an automorphism of $End(F)$, then there is an $\alpha \in Aut(F)$ such that $T(\beta ) = \alpha \circ \beta \circ \alpha ^{-1}$ for all $\beta \in End(F)$.

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