Mathematics – Group Theory
Scientific paper
2009-12-02
Mathematics
Group Theory
20 pages, 6 figures, results are improved. To appear in Osaka J. Math.
Scientific paper
There are natural actions of the braid groups on the products of the braid
groups, called the Hurwitz action. We first study the roots of centralizers in
the braid groups. By using the structure of the roots, we provide a criterion
for the Hurwitz orbit become finite and give an upper bound of the size of a
finite orbit in length 2 or degree 3 case.
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