ELEMENTARY SUBGROUPS OF RELATIVELY HYPERBOLIC GROUPS AND BOUNDED GENERATION
2006 ◽
Vol 16
(01)
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pp. 99-118
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Keyword(s):
Let G be a group hyperbolic relative to a collection of subgroups {Hλ, λ ∈ Λ}. We say that a subgroup Q ≤ G is hyperbolically embedded into G, if G is hyperbolic relative to {Hλ, λ ∈ Λ} ∪ {Q}. In this paper we obtain a characterization of hyperbolically embedded subgroups. In particular, we show that if an element g ∈ G has infinite order and is not conjugate to an element of some Hλ, λ ∈ Λ, then the (unique) maximal elementary subgroup containing g is hyperbolically embedded into G. This allows us to prove that if G is boundedly generated, then G is elementary or Hλ = G for some λ ∈ Λ.
2018 ◽
Vol 2018
(742)
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pp. 79-114
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Keyword(s):
Keyword(s):
2008 ◽
Vol 18
(01)
◽
pp. 97-110
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2013 ◽
Vol 05
(04)
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pp. 451-475
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2015 ◽
Vol 25
(05)
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pp. 689-723
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2008 ◽
Vol 360
(12)
◽
pp. 6303-6318
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2012 ◽
Vol 04
(01)
◽
pp. 99-113
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