منابع مشابه
Steinberg groups as amalgams
For any root system and any commutative ring, we give a relatively simple presentation of a group related to its Steinberg group St. This includes the case of infinite root systems used in Kac–Moody theory, for which the Steinberg group was defined by Tits and Morita–Rehmann. In most cases, our group equals St, giving a presentation with many advantages over the usual presentation of St. This e...
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A nitely presented group G is called metabolic if H 2 (1) (G; A) = 0 for all normed abelian coeecient groups A; it is equivalent to require that a Cayley graph for G admit a thin combing. Metabolicity is stronger than hyperbolicity, and it is an open problem whether all hyperbolic groups are metabolic. We prove that if H is metabolic, then H ha;b]i F(a; b) is also metabolic, where F(a;b) is fre...
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For n ≥ 2 let ∆ be a Dynkin diagram of rank n and let I = {1, . . . , n} be the set of labels of ∆. A group G admits a weak Phan system of type ∆ over C if G is generated by subgroups Ui, i ∈ I , which are central quotients of simply connected compact semisimple Lie groups of rank one, and contains subgroups Ui,j = 〈Ui, Uj〉, i 6= j ∈ I , which are central quotients of simply connected compact s...
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In this paper we will prove analogues of B. Maier’s characterization of weak and strong embeddability of amalgams in N2 [12, 13] for the subvarieties of N2. We will also give analogues of D. Saracino’s characterization of weak and strong amalgamation bases [17], the author’s work on dominions [11] and on amalgamation bases in some varieties of nil-2 groups [8, 9]. Definitions will be recalled b...
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Geometric methods proposed by Stallings [53] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [4, 25, 37, 38, 43, 48, 56]. It turns out that Stallings’ methods can be effectively generalized for the class of amalgams of finite groups [39]. In the present paper we employ subgroup gr...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2016
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2016.10.1791