Ginzburg, Matan; Shusterman, Mark Semi-free subgroups of a profinite surface group. (English) Zbl 1437.20023 J. Group Theory 21, No. 5, 901-910 (2018). Summary: We show that every closed normal subgroup of infinite index in a profinite surface group \(\Gamma\) is contained in a semi-free profinite normal subgroup of \(\Gamma\). This answers a question of L. Bary-Soroker et al. [Math. Res. Lett. 18, No. 3, 459–471 (2011; Zbl 1252.20030)]. MSC: 20E18 Limits, profinite groups 20F65 Geometric group theory 20E05 Free nonabelian groups 20E07 Subgroup theorems; subgroup growth Citations:Zbl 1252.20030 PDFBibTeX XMLCite \textit{M. Ginzburg} and \textit{M. Shusterman}, J. Group Theory 21, No. 5, 901--910 (2018; Zbl 1437.20023) Full Text: DOI arXiv References: [1] L. Bary-Soroker, D. Haran and D. Harbater, Permanence criteria for semi-free profinite groups, Math. Ann. 348 (2010), no. 3, 539-563. · Zbl 1256.20028 [2] L. Bary-Soroker, K. F. Stevenson and P. A. Zalesskii, Subgroups of profinite surface groups, Math. Res. Lett. 18 (2011), no. 3, 459-471. · Zbl 1252.20030 [3] M. D. Fried and M. Jarden, Field Arithmetic, 3rd ed., Ergeb. Math. Grenzgeb. (3) 11, Springer, Berlin, 2008. [4] R. I. Grigorchuk, Branch groups, Mat. Zametki 67 (2000), no. 6, 852-858. · Zbl 0994.20027 [5] A. Pacheco, K. F. Stevenson and P. Zalesskii, Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic, Math. Ann. 343 (2009), no. 2, 463-486. · Zbl 1184.14046 [6] L. Ribes and P. Zalesskii, Profinite Groups, 2nd ed., Ergeb. Math. Grenzgeb. (3) 40, Springer, Berlin, 2010. · Zbl 1197.20022 [7] M. Shusterman, Free subgroups of finitely generated free profinite groups, J. Lond. Math. Soc. (2) 93 (2016), no. 2, 361-378. · Zbl 1403.20040 [8] P. A. Zalesskii, Profinite surface groups and the congruence kernel of arithmetic lattices in {\rm SL}_{2}(\mathbb{R}), Israel J. Math. 146 (2005), 111-123. · Zbl 1076.20020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.