Some Applications of the Wreath Product Construction

1976 ◽  
Vol 83 (5) ◽  
pp. 317 ◽  
Author(s):  
Charles Wells
Keyword(s):  
Wreath Product ◽  
Product Construction

Wreath products along the period-doubling route to chaos

1999 ◽  
Vol 19 (6) ◽  
pp. 1617-1636 ◽  
Author(s):  
J. D. H. SMITH
Keyword(s):  
Wreath Product ◽  
Period Doubling ◽  
Periodic Points ◽  
Wreath Products ◽  
Explicit Description ◽  
Quadratic Maps ◽  
Combinatorial Description ◽  
Product Construction ◽  
Renormalization Operator ◽  
Route To Chaos

The wreath-product construction is used to give a complete combinatorial description of the dynamics of period-doubling quadratic maps leading to the Feigenbaum map. An explicit description of the action on periodic points uses the Thue–Morse sequence. In particular, a wreath-product construction of this sequence is given. The combinatorial renormalization operator on the period-doubling family of maps is invertible.

scholarly journals The persistence of universal formulae in free algebras

1987 ◽  
Vol 36 (1) ◽  
pp. 11-17 ◽  
Author(s):  
Anthony M. Gaglione ◽  
Dennis Spellman
Keyword(s):  
Wreath Product ◽  
Free Algebra ◽  
Variety Of Algebras ◽  
Free Algebras ◽  
Product Construction

Gilbert Baumslag, B.H. Neumann, Hanna Neumann, and Peter M. Neumann successfully exploited their concept of discrimination to obtain generating groups of product varieties via the wreath product construction. We have discovered this same underlying concept in a somewhat different context. Specifically, let V be a non-trivial variety of algebras. For each cardinal α let Fα(V) be a V-free algebra of rank α. Then for a fixed cardinal r one has the equivalence of the following two statements:(1) Fr(V) discriminates V. (1*) The Fs(V) satisfy the same universal sentences for all s≥r. Moreover, we have introduced the concept of strong discrimination in such a way that for a fixed finite cardinal r the following two statements are equivalent:(2) Fr(V) strongly discriminates V. (2*) The Fs(V) satisfy the same universal formulas for all s ≥ r whenever elements of Fr(V) are substituted for the unquantified variables. On the surface (2) and (2*) appear to be stronger conditions than (1) and (1*). However, we have shown that for particular varieties (of groups) (2) and (2*) are no stronger than (1) and (1*).

scholarly journals Wreath Products of Permutation Classes

10.37236/964 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Robert Brignall
Keyword(s):  
Wreath Product ◽  
Wreath Products ◽  
General Construction ◽  
Finitely Based ◽  
Product Construction

A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction $X\wr Y$ of two permutation classes $X$ and $Y$ is also closed, and we exhibit a family of classes $Y$ with the property that, for any finitely based class $X$, the wreath product $X\wr Y$ is also finitely based. Additionally, we indicate a general construction for basis elements in the case where $X\wr Y$ is not finitely based.

EMBEDDABILITY OF GENERALISED WREATH PRODUCTS

2014 ◽  
Vol 91 (2) ◽  
pp. 250-263 ◽  
Author(s):  
CHRIS CAVE ◽  
DENNIS DREESEN
Keyword(s):  
Hilbert Space ◽  
Wreath Product ◽  
Metric Spaces ◽  
Wreath Products ◽  
Finitely Generated ◽  
Product Construction ◽  
Finitely Generated Groups

AbstractGiven two finitely generated groups that coarsely embed into a Hilbert space, it is known that their wreath product also embeds coarsely into a Hilbert space. We introduce a wreath product construction for general metric spaces $X,Y,Z$ and derive a condition, called the (${\it\delta}$-polynomial) path lifting property, such that coarse embeddability of $X,Y$ and $Z$ implies coarse embeddability of $X\wr _{Z}Y$. We also give bounds on the compression of $X\wr _{Z}Y$ in terms of ${\it\delta}$ and the compressions of $X,Y$ and $Z$.

scholarly journals $$H^1$$-conforming finite element cochain complexes and commuting quasi-interpolation operators on Cartesian meshes

CALCOLO ◽  
2021 ◽  
Vol 58 (2) ◽  
Author(s):  
Francesca Bonizzoni ◽  
Guido Kanschat
Keyword(s):  
Finite Element ◽  
Tensor Product ◽  
Arbitrary Order ◽  
Inner Product ◽  
Cochain Complex ◽  
Exterior Derivative ◽  
Product Construction ◽  
Cartesian Meshes ◽  
Conforming Finite Element ◽  
Interpolation Operators

AbstractA finite element cochain complex on Cartesian meshes of any dimension based on the $$H^1$$ H 1 -inner product is introduced. It yields $$H^1$$ H 1 -conforming finite element spaces with exterior derivatives in $$H^1$$ H 1 . We use a tensor product construction to obtain $$L^2$$ L 2 -stable projectors into these spaces which commute with the exterior derivative. The finite element complex is generalized to a family of arbitrary order.

On Commutator Length and Square Length of the Wreath Product of a Group by a Finitely Generated Abelian Group

2010 ◽  
Vol 17 (spec01) ◽  
pp. 799-802 ◽  
Author(s):  
Mehri Akhavan-Malayeri
Keyword(s):  
Abelian Group ◽  
Wreath Product ◽  
Finitely Generated ◽  
Commutator Length

Let W = G ≀ H be the wreath product of G by an n-generator abelian group H. We prove that every element of W′ is a product of at most n+2 commutators, and every element of W2 is a product of at most 3n+4 squares in W. This generalizes our previous result.

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