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

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- by Edward Formanek
- Proc. Amer. Math. Soc.
**130**(2002), 935-937 - DOI: https://doi.org/10.1090/S0002-9939-01-06155-X
- Published electronically: September 14, 2001
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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 $\beta \in End(F)$.*

## References

- Martin R. Bridson and Karen Vogtmann,
*Automorphisms of automorphism groups of free groups*, J. Algebra**229**(2000), no. 2, 785–792. MR**1769698**, DOI 10.1006/jabr.2000.8327 - Joan L. Dyer and Edward Formanek,
*The automorphism group of a free group is complete*, J. London Math. Soc. (2)**11**(1975), no. 2, 181–190. MR**379683**, DOI 10.1112/jlms/s2-11.2.181 - Edward Formanek,
*Characterizing a free group in its automorphism group*, J. Algebra**133**(1990), no. 2, 424–432. MR**1067415**, DOI 10.1016/0021-8693(90)90278-V - D. G. Khramtsov,
*Completeness of groups of outer automorphisms of free groups*, Group-theoretic investigations (Russian), Akad. Nauk SSSR Ural. Otdel., Sverdlovsk, 1990, pp. 128–143 (Russian). MR**1159135** - Vladimir Tolstykh,
*The automorphism tower of a free group*, J. London Math. Soc. (2)**61**(2000), no. 2, 423–440. MR**1760692**, DOI 10.1112/S0024610799008273

## Bibliographic Information

**Edward Formanek**- Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
- Email: formanek@math.psu.edu
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**130**(2002), 935-937 - MSC (2000): Primary 20E05
- DOI: https://doi.org/10.1090/S0002-9939-01-06155-X
- MathSciNet review: 1873764