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


The structure of the automorphism group of a free group on two generators

Author: Dragomir Ž. Đoković
Journal: Proc. Amer. Math. Soc. 88 (1983), 218-220
MSC: Primary 20E05; Secondary 20F28
MathSciNet review: 695245
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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  • [2] Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin-New York, 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89. MR 0577064 (58 #28182)
  • [3] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Wiley, New York, 1966.
  • [4] B. H. Neumann, Die Automorphismengruppe der freien Gruppen, Math. Ann. 107 (1932), 367-386.

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Additional Information

PII: S 0002-9939(1983)0695245-X
Keywords: Free product, semidirect product, automorphisms, finite presentation
Article copyright: © Copyright 1983 American Mathematical Society

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