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Abelian Subgroups of Finitely Generated Kleinian Groups are Separable
Author(s) -
Allman Elizabeth S.,
Hamilton Emily
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460939800530x
Subject(s) - mathematics , kleinian group , abelian group , separable space , orbifold , pure mathematics , finitely generated abelian group , mathematical analysis
By a Kleinian group we mean a discrete subgroup of PSL(2, C). We prove that abelian subgroups of finitely generated Kleinian groups are separable. In other words, if M = H 3 /Γ is a hyperbolic 3‐orbifold, with Γ finitely generated, then abelian subgroups of Γ are separable in Γ. 1991 Mathematics Subject Classification 20E26, 51M10, 57M05.