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Commensurating HNN-extensions: non-positive curvature and biautomaticity
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We show that the commensurator of any quasiconvex abelian subgroup in a biautomatic group is small, in the sense that it has finite image in the abstract commensurator of the subgroup. Using this criterion we exhibit groups that are CAT(0) but not biautomatic. These groups also resolve a number of other questions concerning CAT(0) groups.
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Cited by 2 Pith papers
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Groups of cohomological codimension one
If H is an almost normal subgroup of G, both are of type VFP, and vcd(G)=vcd(H)+1, then G is the fundamental group of a finite graph of groups with vertex and edge groups commensurable to H.
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Erratum and addenda to "Isometry groups of non-positively curved spaces: discrete subgroups"
The authors fix their Euclidean factor theorem for CAT(0) lattices: a lattice always commensurates a free abelian subgroup whose rank equals the Euclidean dimension, and finite generation or residual finiteness recove...
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