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Every virtually cyclic group Γ that surjects onto the infinite dihedral group  D  ∞  contains an index two subgroup ∏ of the formWe show that the Waldhausen Nil-group of Γ vanishes if and only if the Farrell Nil-group of ∏ vanishes.

Relating the Farrell Nil-groups to the Waldhausen Nil-groups