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Actions, wreath products of Cvarieties and concatenation product
 THEORET. COMPUT. SCI
, 2006
"... The framework of Cvarieties, introduced by the third author, extends the scope of Eilenberg’s variety theory to new classes of languages. In this paper, we first define Cvarieties of actions, which are closely related to automata, and prove their equivalence with the original definition of Cvarie ..."
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Cited by 8 (1 self)
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of stamps. Next, we complete the study of the wreath product initiated by Ésik and Ito by extending its definition to Cvarieties in two different ways, which are proved to be equivalent. We also state an extension of the wreath product principle, a standard tool of language theory. Finally, our main result
PROPER ACTIONS OF WREATH PRODUCTS AND GENERALIZATIONS
, 905
"... Abstract. We study stability properties of the Haagerup property and of coarse embeddability in a Hilbert space, under certain semidirect products. In particular, we prove that they are stable under taking standard wreath products. Our construction also allows for a characterization of subsets with ..."
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Cited by 9 (2 self)
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Abstract. We study stability properties of the Haagerup property and of coarse embeddability in a Hilbert space, under certain semidirect products. In particular, we prove that they are stable under taking standard wreath products. Our construction also allows for a characterization of subsets
On Random Walks on Wreath Products
 Ann. Probab
, 2001
"... Wreath products are a type of semidirect products. They play an important role in group theory. This paper studies the basic behavior of simple random walks on such groups and shows that these walks have interesting, somewhat exotic behaviors. The crucial fact is that the probability of return to th ..."
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Cited by 34 (5 self)
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Wreath products are a type of semidirect products. They play an important role in group theory. This paper studies the basic behavior of simple random walks on such groups and shows that these walks have interesting, somewhat exotic behaviors. The crucial fact is that the probability of return
Invariant states on the wreath product
, 903
"... Let S ∞ be the infinity permutation group and Γ be a separable topological group. The wreath product Γ ≀ S ∞ is the semidirect product Γ ∞ e ⋊ S ∞ for the usual permutation action of S ∞ on Γ ∞ e = {[γi] ∞ i=1: γi ∈ Γ, only finitely many γi ̸ = e}. In this paper we obtain the full description of in ..."
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Cited by 1 (0 self)
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Let S ∞ be the infinity permutation group and Γ be a separable topological group. The wreath product Γ ≀ S ∞ is the semidirect product Γ ∞ e ⋊ S ∞ for the usual permutation action of S ∞ on Γ ∞ e = {[γi] ∞ i=1: γi ∈ Γ, only finitely many γi ̸ = e}. In this paper we obtain the full description
Extended Wreath Products
, 2008
"... Let G and Γ be groups acting on sets X and Ψ, respectively. We give explicit formulas for a series of group multiplications on the cartesian product Γ X ×G together with actions on the set of functions Ψ X. These structures form an infinite family of semidirect products Γ X ⋊G parametrized by two in ..."
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Let G and Γ be groups acting on sets X and Ψ, respectively. We give explicit formulas for a series of group multiplications on the cartesian product Γ X ×G together with actions on the set of functions Ψ X. These structures form an infinite family of semidirect products Γ X ⋊G parametrized by two
ON PROPERTY (FA) FOR WREATH PRODUCTS
"... Abstract. We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A ≀ 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 an ..."
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Cited by 3 (1 self)
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Abstract. We characterize permutational wreath products with Property (FA). For instance, the standard wreath product A ≀ 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
GENERATORS AND RELATIONS FOR WREATH PRODUCTS
, 810
"... Abstract. Generators and defining relations for wreath products of groups are given. Under some condition (conormality of the generators) they are minimal. In particular, it is just the case for the Sylow subgroups of the symmetric groups. Let G, H be two groups. Denote by HG the group of all maps f ..."
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Cited by 1 (0 self)
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f: G → H with finite support, i.e. such that f(x) = 1 for all but a finite set of elements of G. Recall that their (restricted regular) wreath product W = H ≀ G is defined as the semidirect product HG ⋊ G with the natural action of G on HG: fg (a) = f(ag) [2, p.175]. We are going to find a set
Compression bounds for wreath products
, 907
"... 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 t ..."
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Cited by 4 (0 self)
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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
Eigenvalues of Random Wreath Products
 Electron. J. Probab
, 2002
"... . Consider a unifomrly chosen element Xn of the nfold wreath product \Gamma n = G o G o \Delta \Delta \Delta o G, where G is a finite permutation group acting transitively on some set of size s. The eigenvalues of Xn in the natural s n  dimensional permutation representation (the composition rep ..."
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Cited by 4 (0 self)
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. Consider a unifomrly chosen element Xn of the nfold wreath product \Gamma n = G o G o \Delta \Delta \Delta o G, where G is a finite permutation group acting transitively on some set of size s. The eigenvalues of Xn in the natural s n  dimensional permutation representation (the composition
On the Integral Cohomology of Wreath Products
, 2007
"... Under mild conditions on the space X, we describe the additive structure of the integral cohomology of the space X p ×Cp ECp in terms of the cohomology of X. We give weaker results for other similar spaces, and deduce various corollaries concerning the cohomology of finite groups. ..."
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Cited by 6 (0 self)
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Under mild conditions on the space X, we describe the additive structure of the integral cohomology of the space X p ×Cp ECp in terms of the cohomology of X. We give weaker results for other similar spaces, and deduce various corollaries concerning the cohomology of finite groups.
Results 1  10
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