All Questions

It is well-known that a subgroup of a hyperbolic group need not be hyperbolic. Let us say that a (finitely generated) group $G$ is locally hyperbolic if all its finitely generated subgroups are (...

Is there an elementary and efficient algorithm for testing the membership to a double coset of f.g. subgroups in a free group? Has this membership problem been implemented in GAP/Magma? More ...

Let $F_X$ be a free group on a countably infinite set $X$. Let $\alpha$ be an automorphism of $F_X$ and $H$ a closed subgroup of $F_X$ in the profinite topology. Is it possible that $\alpha(H) \...

Let $F$ be a free group on a finite set $X$. Let $A \subseteq X$ be a subset of $X$ contained in some $H \leq F$, a subgroup of finite index in $F$. Must there be a basis (free generating set) for $H$ ...

Let $\Gamma_g$ be a surface group of genus $g \geq 2$, that is we have a presentation: $$\Gamma_g = \langle x_1,y_1 \dots, x_g,y_g \vert \prod_{i = 1}^g [x_i,y_i] = 1\rangle$$ Let $H \leq \Gamma_g$ ...

Let $A,B$ be finitely generated groups with a common finite subgroup $C$. Suppose that $[A : C] > 2, [B : C] > 1$. Must $A *_C B$ have positive rank gradient? See Which 3-manifolds have ...