All Questions

Question: Let $G$ be a finitely generated group with exponential growth. Is there a finite generating set $S \subset G$, such that the associated Cayley graph $Cay(G,S)$ contains a binary tree? ...

Is it true that every finitely generated infinite simple group has exponential (word-)growth? Remark: As Mark Sapir has pointed out, the question whether every finitely generated group of ...

Is it true that for every compact hyperbolic $3$-manifold $M$ there exists a prime $p$, a finite field extension $K/\mathbb{Q}_p$, and an injective group homomorphism $$\tau \colon \pi_1(M) \to \...

Mikhail Gromov states that he "tried for about 10 years to prove that every hyperbolic group is realizable by a space of negative curvature" in his interview with Martin Raussen and Christian Skau (...

The Hilbert-Smith Conjecture (HSC) is a famous open problem in geometric group theory stating "for every prime $p$ there are no faithful continuous action of the $p$-adic group of integers $A_p$ ...