On the outer automorphism groups of free groups
Vladimir A. Tolstykh
TL;DR
This paper proves that the outer automorphism group of a countably infinite rank free group is complete, meaning it has no nontrivial automorphisms and a trivial center.
Contribution
It establishes the completeness of the outer automorphism group for free groups of infinite rank, extending understanding of their automorphism structures.
Findings
Outer automorphism group of infinite rank free groups is complete
The group has trivial center and no nontrivial automorphisms
Extends known results from finite to infinite rank cases
Abstract
We prove that the outer automorphism group of a free group of countably infinite rank is complete.
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