The structure of the automorphism group of a free group on two generators
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- by Dragomir Ž. Đoković PDF
- Proc. Amer. Math. Soc. 88 (1983), 218-220 Request permission
Abstract:
Let ${F_2} = Z * Z$ be a free group of rank two. We show that ${\operatorname {Aut} F_2}$ can be built up from cyclic groups by using only the free products and semidirect products. Explicitly we have $\operatorname {Aut} {F_2} = ((Z * Z) \rtimes ({Z_3} * {Z_3})) \rtimes ({Z_4} \rtimes {Z_2})$. As a corollary we obtain a simple presentation of $\operatorname {Aut} {F_2}$.References
- H. S. M. Coxeter and W. O. J. Moser, Generators and relations for discrete groups, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 14, Springer-Verlag, New York-Heidelberg, 1972. MR 0349820, DOI 10.1007/978-3-662-21946-1
- Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89, Springer-Verlag, Berlin-New York, 1977. MR 0577064 W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Wiley, New York, 1966. B. H. Neumann, Die Automorphismengruppe der freien Gruppen, Math. Ann. 107 (1932), 367-386.
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 218-220
- MSC: Primary 20E05; Secondary 20F28
- DOI: https://doi.org/10.1090/S0002-9939-1983-0695245-X
- MathSciNet review: 695245