Loop subgroups of \(F_r\) and the image of their stabilizer subgroups in \(\mathrm{GL}_r(\mathbb Z)\).

DOI10.1007/s11856-011-0213-3zbMath1292.20030arXiv1012.2729OpenAlexW1976466195MaRDI QIDQ375801

Joachim Breitner

Publication date: 1 November 2013

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2729

zbMATH Keywords

free groupscongruence subgroupscoset graphsloop subgroups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Structure of modular groups and generalizations; arithmetic groups (11F06) Free nonabelian groups (20E05) Teichmüller theory for Riemann surfaces (30F60)

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Cites Work

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• Arithmetic Veech sublattices of SL\((2,\mathbf {Z})\)
• The congruence subgroup problem. An elementary approach aimed at applications.
• An Algorithm for Finding the Veech Group of an Origami
• Noncongruence subgroups in H(2)
• The probability of generating the symmetric group

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