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On intersections of conjugate subgroups.

We define a new invariant of a conjugacy class of subgroups which we call the weak width and prove that a quasiconvex subgroup of a negatively curved group has finite weak width in the ambient group. Utilizing the coset graph and the geodesic core of a subgroup we give an explicit algorithm for constructing a finite generating set for an intersection of a quasiconvex sub-group of a negatively curved group with a conjugate. Using that algorithm we construct algorithms for computing the weak width, the width and the height of a quasiconvex subgroup of a negatively curved group. These algorithms decide if a quasiconvex subgroup of a negatively curved group is almost malnormal in the ambient group.