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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Edward Formanek
Journal: Proc. Amer. Math. Soc. 130 (2002), 935-937
MSC (2000): Primary 20E05
Published electronically: September 14, 2001
MathSciNet review: 1873764
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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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Additional Information

Edward Formanek
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: formanek@math.psu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06155-X
PII: S 0002-9939(01)06155-X
Keywords: Free group, endomorphism, automorphism
Received by editor(s): October 2, 2000
Published electronically: September 14, 2001
Additional Notes: The author was partially supported by the NSF
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2001 American Mathematical Society