3 problems

The small sphere hypothesis implies the small gap property
Small sphere to small gap conjecture. Then $G$ has the SG property. The SG property would provide the ball-intersection control needed for the SBM theory; it is known for…
openadditive-combinatorics geometric-group-theory virtually-nilpotent-groups
0 responses
07
Virtually nilpotent groups' profile equivalence conjecture
Let $G$ be a finitely generated virtually nilpotent group, let $S$ be a finite generating set, and let $\mathcal{D}_{G,S}^{sof}$ , $\mathcal{D}_{G,S}^{hyp}$ ,…
opengroup-profiles sofic-groups virtually-nilpotent-groups
0 responses
08
Nekrashevych–Pete's conjecture on strongly scale-invariant groups
A finitely generated group $\Gamma$ is strongly scale-invariant if there exists an embedding $\varphi:\Gamma\hookrightarrow\Gamma$ with image of finite index and such that … is fin…
opengroup-theory scale-invariant-groups virtually-nilpotent-groups
0 responses
06

The small sphere hypothesis implies the small gap property