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The Free Group F 2

In: Markov's Theorem and 100 Years of the Uniqueness Conjecture

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  • Martin Aigner

    (Freie Universität Berlin, Fachbereich Mathematik und Informatik Institut für Mathematik)

Abstract

In the previous chapter, we saw that every two Cohn matrices of a Cohn triple generate the same subgroup of SL( $$2, \mathbb{Z}$$ ), namely the commutator subgroup SL( $$2, \mathbb{Z}$$ )’. This group turns out to have a very interesting structure leading to a new interpretation of the Cohn matrices as combinatorial words. On the way, we get to know the basics of free groups, prove a classical theorem about automorphisms of free groups, and see how the Cohn matrices can be used to solve an interesting problem describing primitive elements in the free group of rank 2.

Suggested Citation

  • Martin Aigner, 2013. "The Free Group F 2," Springer Books, in: Markov's Theorem and 100 Years of the Uniqueness Conjecture, edition 127, chapter 6, pages 113-131, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-00888-2_6
    DOI: 10.1007/978-3-319-00888-2_6
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