On finitely presented metabelian groups
نویسندگان
چکیده
منابع مشابه
Subgroups of Finitely Presented Centre-by-metabelian Groups
1.1. Baumslag's theorem has another facet. It shows that in the variety 2l of metabelian groups, every finitely generated $I-group G occurs as a subgroup of some finitely presented 2I-group G. The analogous result for the variety of all groups is a celebrated theorem of G. Higman [8] which states that a finitely generated group G is the subgroup of a finitely presented group G if, and only if, ...
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Given a finite presentation of a group G, proving properties of G can be difficult. Indeed, many questions about finitely presented groups are unsolvable in general. Algorithms exist for answering some questions while for other questions algorithms exist for verifying the truth of positive answers. An important tool in this regard is the Todd-Coxeter coset enumeration procedure. It is possible ...
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Algorithms are constructed which, when an explicit presentation of a finitely generated metabelian group G in the variety si1 is given, produce unitary presentations for the derived subgroup G', the centre Z{G), the Fitting subgroup Fit(G), and the Frattini subgroup <p(G). Additional algorithms of independent interest are developed for commutative algebra which construct the associated set of p...
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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: Bulletin of the American Mathematical Society
سال: 1972
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1972-12958-6