3 problems

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Free-subgroup conjecture for finitely presented Golod–Shafarevich groups
Let $G$ be a finitely presented Golod–Shafarevich abstract group. Free-subgroup conjecture. The group $G$ contains a non-abelian free subgroup. The source states this as a positive…
Conjectureopenfree-groups golod-shafarevich-groupsarXiv posted 2 days ago
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Lubotzky's conjecture on property $(T)$ quotients of Golod–Shafarevich groups
A Golod–Shafarevich group is a group arising from a Golod–Shafarevich presentation. Lubotzky's conjecture. Every Golod–Shafarevich group should have an infinite quotient with prope…
Conjectureopengolod-shafarevich-groups group-theory kazhdan-propertyarXiv posted 2 days ago
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Wilson's free-subgroup conjecture for Golod–Shafarevich groups
A discrete group or pro- $p$ group is said to violate the Golod–Shafarevich inequality when its presentation does not satisfy that inequality. Wilson's conjecture. Every discrete gr…
Conjecturesolvedgolod-shafarevich-groups group-theory pro-p-groupsarXiv posted 2 days ago

Free-subgroup conjecture for finitely presented Golod–Shafarevich groups