Weak Width of Subgroups

الأصل · EN

We say that the weak width of an infinite subgroup H of G in G is n if there exists a collection of n strongly essentially distinct conjugates { H, g₁⁻¹ H g₁,, gₙ₋₁⁻¹ H gₙ₋₁ } of H in G such that the intersection H ∩ gᵢ⁻¹ H gᵢ is infinite for all 1 ≤ i ≤ n-1 and n is maximal possible. We prove that a quasiconvex subgroup of a negatively curved group has finite weak width in the ambient group. We also give examples demonstrating that height, width, and weak width are different invariants of a subgroup.