Ascending HNN extensions of polycyclic groups are residually finite
نویسندگان
چکیده
منابع مشابه
A CRITERION FOR HNN EXTENSIONS OF FINITE p-GROUPS TO BE RESIDUALLY p
We give a criterion for an HNN extension of a finite p-group to be residually p. 1. Statement of the Main Results By an HNN pair we mean a pair (G,φ) where G is a group and φ : A → B is an isomorphism between subgroups A and B of G. Given such an HNN pair (G,φ) we consider the corresponding HNN extension G∗ = 〈G, t | t−1at = φ(a), a ∈ A〉 of G, which we denote, by slight abuse of notation, as G∗...
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is called an ascending HNN extension of G (or the mapping torus of the endomorphism φ). In particular, the ascending HNN extensions of free groups of finite rank are simply the groups given by presentations 〈x1, ..., xn, t | txit−1 = wi, i = 1, ..., n〉, where w1, ..., wn are words generating a free subgroup of rank n. In [BS], Borisov and Sapir proved that all ascending HNN extensions of linear...
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Definition 1. Let G be a group. G is said to be residually finite if the intersection of all normal subgroups of G of finite index in G is trivial. For a survey of results on residual finiteness and related properties, see Mag-nus, Karrass, and Solitar [6, Section 6.5]. We shall present a proof of the following well known theorem, which is important for Kharlampovich [4, 5]. See also O. V. Bele...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2003
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(02)00310-9