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• W2748692956 startingPage "4163" @default.
• W2748692956 abstract "We establish three independent results on groups acting on trees. The first implies that a compactly generated locally compact group which acts continuously on a locally finite tree with nilpotent local action and no global fixed point is virtually indicable; that is to say, it has a finite index subgroup which surjects onto $mathbf{Z}$. The second ensures that irreducible cocompact lattices in a product of non-discrete locally compact groups such that one of the factors acts vertex-transitively on a tree with a nilpotent local action cannot be residually finite. This is derived from a general result, of independent interest, on irreducible lattices in product groups. The third implies that every non-discrete Burger-Mozes universal group of automorphisms of a tree with an arbitrary prescribed local action admits a compactly generated closed subgroup with a non-discrete simple quotient. As applications, we answer a question of D. Wise by proving the non-residual finiteness of a certain lattice in a product of two regular trees, and we obtain a negative answer to a question of C. Reid, concerning the structure theory of locally compact groups." @default.
• W2748692956 created "2017-08-31" @default.
• W2748692956 creator A5067961087 @default.
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• W2748692956 date "2018-12-06" @default.
• W2748692956 modified "2023-10-16" @default.
• W2748692956 title "Indicability, residual finiteness, and simple subquotients of groups acting on trees" @default.
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• W2748692956 doi "https://doi.org/10.2140/gt.2018.22.4163" @default.
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