Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nombre de classes de conjugaison d'\'el\'ements d'ordre fini dans les
  groupes de Brown-Thompson   We extend a result of Matucci on the number of conjugacy classes of finite
order elements in the Thompson group $T$. According to Liousse, if $
gcd(m-1,q)$ is not a divisor of $r$ then there does not exist element of order
$q$ in the Brown-Thompson group $T_{r,m}$. We show that if $ gcd(m-1,q)$ is a
divisor of $r$ then there are exactly $\varphi(q). gcd(m-1,q)$ conjugacy
classes of elements of order $q$ in $T_{r,m}$, where $\varphi$ is the Euler
function phi. As a corollary, we obtain that the Thompson group $T$ is
isomorphic to none of the groups $T_{r,m}$, for $m\not=2$ and any morphism from
$T$ into $T_{r,m}$, with $m\not=2$ and $r\not= 0$ $mod \ (m-1)$, is trivial.

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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat