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An alternate proof of Wise’s malnormal special quotient theorem. (English) Zbl 1380.20047

Summary: We give an alternate proof of D. T. Wise’s [“The structure of groups with a quasiconvex hierarchy”, Preprint] malnormal special quotient theorem (MSQT), avoiding cubical small cancelation theory. We also show how to deduce Wise’s [loc. cit.] Quasiconvex Hierarchy Theorem from the MSQT and theorems of T. Hsu and D. T. Wise [Invent. Math. 199, No. 2, 293–331 (2015; Zbl 1320.20039)] and F. Haglund and D. T. Wise [Ann. Math. (2) 176, No. 3, 1427–1482 (2012; Zbl 1277.20046)].

MSC:

20F67 Hyperbolic groups and nonpositively curved groups
20E08 Groups acting on trees
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