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The orbits of the Hurwitz action of the braid groups on the standard generators

Yoshiro Yaguchi — 2010

Fundamenta Mathematicae

The Hurwitz action of the n-braid group Bₙ on the n-fold direct product $(B_{m}) ⁿ$ of the m-braid group $B_{m}$ is studied. We show that the orbit of any n- tuple of the n standard generators of $B_{n + 1}$ consists of the (n-1)th powers of n+1 elements.

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