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

Volume 210 / 2010

Yoshiro Yaguchi Fundamenta Mathematicae 210 (2010), 63-71 MSC: Primary 20F36; Secondary 20F05. DOI: 10.4064/fm210-1-3

Abstract

The Hurwitz action of the $n$-braid group $B_n$ 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.

Authors

  • Yoshiro YaguchiDepartment of Mathematics
    Hiroshima University
    Higashi-Hiroshima, 739-8526 Japan
    e-mail

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