Expand all Collapse all | Results 1 - 2 of 2 |
1. CMB 2012 (vol 56 pp. 570)
Conjugacy Classes and Binary Quadratic Forms for the Hecke Groups In this paper we give a lower bound
with respect to block length
for the trace of non-elliptic conjugacy classes
of the Hecke groups.
One consequence of our bound
is that there are finitely many
conjugacy classes of a given trace in any Hecke group.
We show that another consequence of our bound
is that
class numbers are finite for
related hyperbolic \( \mathbb{Z}[\lambda] \)-binary quadratic forms.
We give canonical class representatives
and calculate class numbers
for some classes of hyperbolic \( \mathbb{Z}[\lambda] \)-binary quadratic forms.
Keywords:Hecke groups, conjugacy class, quadratic forms Categories:11F06, 11E16, 11A55 |
2. CMB 2012 (vol 57 pp. 132)
Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups Given a group automorphism $\phi:\Gamma\longrightarrow \Gamma$, one has
an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$.
The orbits of this action are called $\phi$-twisted conjugacy classes. One says
that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-twisted conjugacy
classes for every automorphism $\phi$ of $\Gamma$. In this paper we
show that $\operatorname{SL}(n,\mathbb{Z})$ and its
congruence subgroups have the $R_\infty$-property. Further we show that
any (countable) abelian extension of $\Gamma$ has the $R_\infty$-property where $\Gamma$ is a torsion
free non-elementary hyperbolic group, or $\operatorname{SL}(n,\mathbb{Z}),
\operatorname{Sp}(2n,\mathbb{Z})$ or a principal congruence
subgroup of $\operatorname{SL}(n,\mathbb{Z})$ or the fundamental group of a complete Riemannian
manifold of constant negative curvature.
Keywords:twisted conjugacy classes, hyperbolic groups, lattices in Lie groups Category:20E45 |