Howie, James; Saeed, Muhammad Sarwar Freiheitssätze for one-relator quotients of surface groups and of limit groups. (English) Zbl 1183.20041 Q. J. Math. 60, No. 3, 313-325 (2009). Authors’ summary: Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are natural extensions of previously published corresponding statements for one-relator quotients of orientable surface groups. Two of the proofs are new even in that restricted context. Reviewer: Gerhard Rosenberger (Dortmund) Cited in 2 Documents MSC: 20F65 Geometric group theory 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 20F05 Generators, relations, and presentations of groups 20E08 Groups acting on trees 20E18 Limits, profinite groups 57M07 Topological methods in group theory Keywords:Freiheitssatz; one-relator quotients; limit groups; acylindrical group actions; orientable surface groups PDFBibTeX XMLCite \textit{J. Howie} and \textit{M. S. Saeed}, Q. J. Math. 60, No. 3, 313--325 (2009; Zbl 1183.20041) Full Text: DOI arXiv