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PreprintarXiv licencearXiv

Ivanov's finite-index Frattini conjecture for subgroups of mapping class groups

  • Renaud Detcherry
  • Efstratia Kalfagianni
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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, using recent partial results of the first author about the Andersen-Masbaum-Ueno conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{detcherry2026ivanovs,
  title = {{Ivanov's finite-index Frattini conjecture for subgroups of mapping class groups}},
  author = {Renaud Detcherry and Efstratia Kalfagianni},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01734},
  eprint = {2610.01734},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01734},
}
RIS
TY  - UNPB
TI  - Ivanov's finite-index Frattini conjecture for subgroups of mapping class groups
AU  - Renaud Detcherry
AU  - Efstratia Kalfagianni
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.01734
UR  - https://arxiv.org/abs/2610.01734
AB  - Let S_g be a closed oriented surface of genus g. Ivanov conjectured that if G a finitely generated subgroup of Mod(S_g) its finite-index Frattini subgroup Φ_f(G) is nilpotent. We prove this conjecture, using recent partial results of the first author about the Andersen-Masbaum-Ueno conjecture.
ER  -