منابع مشابه
On Property (fa) for Wreath Products
We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A o B of two nontrivial countable groups A,B has Property (FA) if and only if B has Property (FA) and A is a finitely generated group with finite abelianisation. We also prove an analogous result for hereditary Property (FA). On the other hand, we prove that many wreath products with here...
متن کاملTwo results on wreath products
Among the familiar basic facts concerning unrestricted permutational wreath products (sketched in the first few paragraphs of the last section of Cossey, Kegel, and Kov~cs [2]), the Embedding Theorem has the central role. It asserts the existence of an embedding; the proof is a construction which involves arbitrarily chosen coset representatives, with the effect that the embedding constructed m...
متن کاملKnapsack Problems for Wreath Products
In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under...
متن کاملZonal polynomials for wreath products
The pair of groups, symmetric group S2n and hyperoctohedral group Hn , form a Gelfand pair. The characteristic map is a mapping from the graded algebra generated by the zonal spherical functions of (S2n, Hn) into the ring of symmetric functions. The images of the zonal spherical functions under this map are called the zonal polynomials. A wreath product generalization of the Gelfand pair (S2n, ...
متن کاملCompression bounds for wreath products
We show that if G and H are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath G ≀ H . We also prove an analogous result for coarse embeddings of wreath products. In the special case G = Z, H = Z ≀ Z our result implies that the Hilbert compression exponent of Z ≀ (Z ≀ Z) is at least 1/4, answering a question posed ...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2011
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2010.044