All Questions

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\Aut{Aut}$Does there exist a finitely presented subgroup of $\GL(n,\mathbb{Z})$ for which it is known that the conjugacy problem is unsolvable (if yes, ...

Let $G$ be a group. Suppose for any general linear representation $\rho:G\to\mathrm{GL}(n)$, $\rho$ must be trivial. Question: Are there any characterizations or equivalent conditions for $G$? Thanks ...

Let $g_1(x,y,z)=(y,x,-z), g_2(x,y,z)=(y,x+y+2z,-y-z)$, $V= \{(x,y,z)\in Z^3|xy-z^2+1=0 \}$. Is it possible to find all orbits of the action of group $\langle g_1 \rangle * \langle g_2 \rangle$ on $V$? ...

This question is in reference to this paper, http://annals.math.princeton.edu/wp-content/uploads/annals-v182-n1-p07-p.pdf (or its arxiv version, http://arxiv.org/abs/1304.4132) For the argument to ...

As title. the exponent of $G$ is the least number $n$ (if exists) such that $g^n=e$ holds for all $g\in G$ or $+\infty$.