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33 votes
1 answer
1k views

Is this conjecture strictly weaker than P=NP?

My three computability questions are related to the following group theory question (first asked by Bridson in 1996): For which real $\alpha\ge 2$ the function $n^\alpha$ is equivalent to the Dehn ...
user avatar
21 votes
4 answers
2k views

Is there a non-Hopfian lacunary hyperbolic group?

The question's in the title and is easily stated, but let me try to give some details and explain why I'm interested. First, a disclaimer: if the answer's not already somewhere in the literature then ...
HJRW's user avatar
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6 votes
1 answer
226 views

Are $G$-limits of a slender group $G$ in the space of marked groups also slender?

A group $G$ is slender if every subgroup $H \leq G$ is finitely generated. This includes polycyclic-by-finite groups. Such groups are also called noetherian. Suppose that $L$ is a $G$-limit group in ...
NWMT's user avatar
  • 1,033
3 votes
1 answer
374 views

Is a finitely generated residually free group "almost LERF"?

Let $G$ be a finitely generated residually free group. (i.e. for each $1 \neq g \in G$ there exists a homomorphism $\tau \colon G \to F$ such that $F$ is a free group, and $\tau(g) \neq 1$.) Let $...
Pablo's user avatar
  • 11.3k