. Chapter, A combination theorem for boundaries of groups. does v, which is absurd by construction of (g n )

. Proof, The group G is a convergence group on ?G by Corollary V.2.6, and every point of ?G is conical by LemmaV.2.7, thus the result follows from Theorem I.3.22

. Proof, It is enough to prove the result for the stabiliser of a vertex v of X. Notice that, by Proposition IV.5.19, the boundary of G v embeds G v -equivariantly in ?G, the latter being G-equivariantly homeomorphic to the Gromov boundary of G by Corollary V.2.8. Hence, the result follows from Theorem I, p.28

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