Mathematical Research Letters

Volume 18 (2011)

Number 3

Subgroups of profinite surface groups

Pages: 459 – 471



Lior Bary-Soroker (Universität Duisburg-Essen, Ellernstrasse 29, D-45326 Essen, Germany)

Katherine F. Stevenson (California State University Northridge, 18111 Nordhoff St Northridge, CA 91330-8313, USA)

Pavel A. Zalesskii (University of Brasília, Brasília-DF 70910-900, Brazil)


We study the subgroup structure of the étale fundamental group $\Pi$ of a projective curve over an algebraically closed field of characteristic $0$. We obtain an analog of the diamond theorem for $\Pi$. As a consequence we show that most normal subgroups of infinite index are semi-free. In particular every proper open subgroup of a normal subgroup of infinite index is semi-free.

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