4 problems

Existence of a Hopfian finitely presented group with undecidable weak Whitehead problem
A Hopfian finitely presented group is a finitely presented group for which every surjective endomorphism is an automorphism; its word problem asks whether a given word represents t…
opencomputable-structure-theory decision-problems finitely-presented-groups
0 responses
08
Finite presentability conjecture for finitely generated non-elementary subgroups of $\operatorname{PSL}(2,\mathbb{R})$
Finite presentability conjecture. Then $H$ is finitely presented.
opendiscrete-groups finitely-presented-groups geometric-group-theory
0 responses
08
Grigorchuk's stronger conjecture for finitely presented groups
Let $G$ be a finitely presented group. A free subsemigroup on two generators is a subsemigroup generated by two elements with no nontrivial relations. Grigorchuk's stronger conject…
openfinitely-presented-groups group-growth
0 responses
03
The embeddability-complexity conjecture for finitely presented groups
Embeddability-complexity conjecture. The set $K$ is $\Sigma^0_3$ -complete. Equivalently, deciding whether $\overline{P}_i$ embeds into $\overline{P}_j$ for finite presentations…
opencomputability-theory embeddability finitely-presented-groups
0 responses
04

Existence of a Hopfian finitely presented group with undecidable weak Whitehead problem