1. CMB 2012 (vol 56 pp. 570)
 Hoang, Giabao; Ressler, Wendell

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 nonelliptic 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)
 Mubeena, T.; Sankaran, P.

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 nonelementary 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 
