- 1.
- Fixed subgroups of automorphisms of free by finite groups, Arch. Math.
48 (1987), 25-30.
- 2.
- On graphs realizing automorphisms of free groups, Proc. Amer. Math. Soc.
107 (1989), 573-575.
- 3.
- On the rank of the fixed point set of
automorphisms of free groups (with W. Imrich and E. C. Turner), Circles and
Rays (G. Hahn et al., eds) Kluwer,
Dordrecht 1989.

*SUMMARY:*

Gersten was the first to prove that the fixed point subgroup of an
automorphism of *F*_{n} is finitely generated [G]. The existence of a specific
graph realizing a given automorphism (``Gersten bridge'') was reproved by
several autors; the shortest proof is in my article [2].
Analyzing the Goldstein-Turner's proof of Gersten's Theorem [GT], we
obtain in [3] a bound
for the rank of the fixed-point subgroup. (The same bound was also proved in
[CL].) I also noticed that Cooper's
proof of the Gersten's Theorem [C] generalizes to virtually free groups
[1]. Later, Paulin
showed that, in fact, the generalization goes on to cover the whole class of
hyperbolic groups [P].

*REFERENCES:*

- [C]
- D. Cooper, Automorphisms of free groups
have finitely generated fixed point set, J. Algebra 111
(1987), 453-456.
- [M]
- M. Cohen and M. Lustig, On the dynamics and the fixed subgroup of a
free group automorphism, Inventiones Math. 96 (1989), 613-638.
- [G]
- S. M. Gersten, Fixed points of automorphisms of free
groups, Adv. in Math. 64 (1987), 51-85.
- [GT]
- R. Z. Goldstein and E. C. Turner, Fixed subgroups of
homomorphisms of free groups, Bull. London Math. Soc. 18
(1986), 468-470.
- [P]
- F. Paulin, Points fixes des automorphismes de groupes
hyperboliques, Ann. Inst. Fourier 39 (1989), 651-662.