3 problems

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Benjamini's polynomial-growth conjecture for scale-invariant groups
Let $G$ be a finitely generated group. It is scale-invariant if it has a descending chain $\{G_k\}_{k\geq 0}$ of finite-index subgroups such that each $G_k$ is isomorphic to $G$ an…
Conjecturerefutedgeometric-group-theory group-growth scale-invariant-groupsarXiv posted 2 days ago
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The Benjamini-Nekrashevych-Pete conjecture on strongly scale-invariant groups
Let $G$ be a finitely generated group. A group is strongly scale-invariant if it admits an injective homomorphism $f:G\to G$ such that $f(G)$ is a proper finite-index subgroup of…
Conjecturerefutedgeometric-group-theory nilpotent-groups scale-invariant-groupsarXiv posted 2 days ago
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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…
Conjectureopengroup-theory scale-invariant-groups virtually-nilpotent-groupsarXiv posted 2 days ago

Benjamini's polynomial-growth conjecture for scale-invariant groups