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- W3004675992 abstract "A non-trivial finitely generated pro-$p$ group $G$ is said to be strongly hereditarily self-similar of index $p$ if every non-trivial finitely generated closed subgroup of $G$ admits a faithful self-similar action on a $p$-ary tree. We classify the solvable torsion-free $p$-adic analytic pro-$p$ groups of dimension less than $p$ that are strongly hereditarily self-similar of index $p$. Moreover, we show that a solvable torsion-free $p$-adic analytic pro-$p$ group of dimension less than $p$ is strongly hereditarily self-similar of index $p$ if and only if it is isomorphic to the maximal pro-$p$ Galois group of some field that contains a primitive $p$-th root of unity. As a key step for the proof of the above results, we classify the 3-dimensional solvable torsion-free $p$-adic analytic pro-$p$ groups that admit a faithful self-similar action on a $p$-ary tree, completing the classification of the 3-dimensional torsion-free $p$-adic analytic pro-$p$ groups that admit such actions." @default.
- W3004675992 created "2020-02-14" @default.
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- W3004675992 date "2020-02-06" @default.
- W3004675992 modified "2023-09-27" @default.
- W3004675992 title "On hereditarily self-similar $p$-adic analytic pro-$p$ groups" @default.
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