Remarks on a theorem of Swarup on ends of pairs of groups

  • Kropholler P
  • Roller M
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We give an algebraic proof of a recent theorem of Swarup, which states that if H is a subgroup of infinite index in a finitely generated group G and if e(G, N) = 1 for all subgroups N ◁ H with H/N ≅ ℤ, then e(G, H) = 1 + rank H1(G, ℤ [H\G]). We also consider some generalizations of this theorem.

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  • Peter H. Kropholler

  • Martin A. Roller

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