2 problems

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The positive-dimensional subgroup conjecture in automorphism groups of rooted trees
Let $\Gamma(p)$ be the profinite automorphism group of the rooted $p$ -ary tree, and let positive-dimensional mean having positive Hausdorff dimension as a closed subgroup of…
Conjectureopenfree-pro-p-groups hausdorff-dimension pro-p-groupsarXiv posted 2 days ago
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The free pro-p subgroup conjecture for just infinite branch groups
A just infinite pro- $p$ group is a pro- $p$ group in which every proper quotient is finite, and a branch group is a just infinite pro- $p$ group of branch type. A nonabelian free pro…
Conjectureopenbranch-groups free-pro-p-groups pro-p-groupsarXiv posted 2 days ago

The positive-dimensional subgroup conjecture in automorphism groups of rooted trees