Ivanov's finite-index Frattini subgroup conjecture for subgroups of the Torelli group
Renaud Detcherry
Abstract
Let Sg be a closed oriented surface of genus g. Ivanov conjectured that if G a finitely generated subgroup of Mod(Sg) its finite-index Frattini subgroup Φf(G) is nilpotent. We prove this conjecture for finitely generated subgroups of the Torelli subgroup J1(Sg), 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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