Ivanov’s finite-index Frattini subgroup conjecture
For every genus and every finitely generated subgroup , where is a closed oriented surface, the finite-index Frattini subgroup is nilpotent.
References
Primary source
Additional references
- Ivanov's finite-index Frattini subgroup conjecture for subgroups of the Torelli group — arXiv — Renaud Detcherry
Progress summary
A new preprint claims progress for subgroups of the Torelli group, but the conjecture for arbitrary finitely generated mapping-class-group subgroups remains open.
Ivanov’s conjecture asks whether the finite-index Frattini subgroup is trivial for every finitely generated subgroup of a mapping class group. The general case remains unresolved.
Known results
For , earlier work records triviality for the closed mapping class group, the Torelli group, the Johnson kernel, and subgroups containing a finite-index subgroup of the Torelli group.
October 2026 Torelli-subgroup advance
A preprint by Renaud Detcherry claims the conjecture for finitely generated subgroups of the Torelli group and records an implication from the full Andersen–Masbaum–Ueno conjecture. This is a claimed advance, not independently verified here; the arbitrary-subgroup case remains open.
Current status (as of October 2026): the conjecture is claimed for finitely generated subgroups of the Torelli group, while the case of arbitrary finitely generated subgroups of the mapping class group remains open.
Sources
Solutions 0
No solutions have been posted yet.