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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
DOI: https://doi.org/10.1090/S0002-9939-1983-0695245-X
MathSciNet review: 695245
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0695245-X
Keywords: Free product, semidirect product, automorphisms, finite presentation
Article copyright: © Copyright 1983 American Mathematical Society

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