Conjugacy Separability of Some One-Relator Groups
نویسندگان
چکیده
منابع مشابه
Conjugacy Separability of Some One-Relator Groups
Conjugacy separability of any group of the class of one-relator groups given by the presentation a, b; a m , b n 1m, n > 1 is proven. The proof made used of theoretical combinatorial group methods, namely the structure of amalgamated free products and some properties of the subgroups and quotients of any group of the class of one-relator groups given above.
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Conjugacy separability of any group of the class of one-relator groups given by the presentation 〈a, b; [am, bn] = 1〉 (m, n > 1) is proven.
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Following Malcev [5], we will call a subgroup M of a group G finitely separable if for any element g ∈ G, not belonging to M, there exists a homomorphism φ of group G onto some finite group X such that gφ / ∈Mφ. This is equivalent to the statement that for any element g ∈ G \M, there exists a normal subgroup N of finite index in G such that g / ∈MN . A group G is subgroup separable if each of i...
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If S is noncompact, or has nonempty boundary, then π1(S) is free, and the answer to Question 1 is yes, by an old result of Magnus [7] on one-relator groups. (Essentially, the defining relator in a one-relator group on a given generating set is unique up to conjugacy and inversion.) We will show (see Theorem 3.4 below) that Question 1 also has an affirmative answer in the case of a closed surfac...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2010
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2010/803243