Finitely Presented Wreath Products and Double Coset Decompositions
نویسندگان
چکیده
منابع مشابه
Finitely Presented Wreath Products and Double Coset Decompositions
We characterize which permutational wreath products G⋉W (X) are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X. On the one hand, this extends a result of G. Baumslag about infinite presentation of standard wreath products; on the other hand, this provides nont...
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Wreath products such as Z ≀ Z are not finitely-presentable yet can occur as subgroups of finitely presented groups. Here we compute the distortion of Z ≀ Z as a subgroup of Thompson’s group F and as a subgroup of Baumslag’s metabelian group G. We find that Z ≀ Z is undistorted in F but is at least exponentially distorted in G.
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In this paper we discuss the splitting or decomposing of finitely generated groups into free products, free products with amalgamation or HNN extensions and we discuss the JSJ decomposition of finitely presented groups.
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The coset and double-coset decompositions of the 420 subgroups of m(z)3(xyz)m(xy)1' (O(h)1') and the 236 subgroups of 6(z)/m(z)m(x)m(1)1' (D(6h)1') with respect to each of their subgroups are calculated along with additional mathematical properties of these groups.
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A JSJ-splitting of a group G over a certain class of subgroups is a graph of groups decomposition of G which describes all possible decompositions of G as an amalgamated product or an HNN extension over subgroups lying in the given class. Such decompositions originated in 3-manifold topology. In this paper we generalize the JSJ-splitting constructions of Sela, Rips-Sela and Dunwoody-Sageev and ...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2006
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-006-9061-4