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arXiv · 2610.01734

Ivanov's finite-index Frattini subgroup conjecture for subgroups of the Torelli group

Renaud Detcherry
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Abstract

Let $S_g$ be a closed oriented surface of genus $g$. Ivanov conjectured that if $G$ a finitely generated subgroup of $\mathrm{Mod}(S_g)$ its finite-index Frattini subgroup $Φ_f(G)$ is nilpotent. We prove this conjecture for finitely generated subgroups of the Torelli subgroup $J_1(S_g)$, using recent partial results of the author about the Andersen-Masbaum-Ueno conjecture. We also show that the full AMU conjecture would imply Ivanov's conjecture.

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Renaud Detcherry. 2026-10-01. Ivanov's finite-index Frattini subgroup conjecture for subgroups of the Torelli group. https://arxiv.org/abs/2610.01734

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