A semicomplete standard wreath product

1984 ◽  
Vol 43 (4) ◽  
pp. 301-302 ◽  
Author(s):  
John Panagopoulos
Keyword(s):  
Wreath Product ◽  
Standard Wreath Product

scholarly journals Minimal generating sets for some wreath products of groups

1973 ◽  
Vol 9 (1) ◽  
pp. 127-136
Author(s):  
Yeo Kok Chye
Keyword(s):  
Abelian Group ◽  
Nilpotent Group ◽  
Wreath Product ◽  
Wreath Products ◽  
Finitely Generated ◽  
Generating Set ◽  
Generating Sets ◽  
Products Of Groups ◽  
Minimal Generating Set ◽  
Standard Wreath Product

Let d(G) denote the minimum of the cardinalities of the generating sets of the group G. Call a generating set of cardinality d(G) a minimal generating set for G. If A is a finitely generated nilpotent group, B a non-trivial finitely generated abelian group and A wr B is their (restricted, standard) wreath product, then it is proved (by explicitly constructing a minimal generating set for A wr B ) that d(AwrB) = max{l+d(A), d(A×B)} where A × B is their direct product.

Automorphisms of permutational wreath products

1978 ◽  
Vol 26 (2) ◽  
pp. 198-208 ◽  
Author(s):  
A. Mohammadi Hassanabadi
Keyword(s):  
Automorphism Group ◽  
Wreath Product ◽  
Wreath Products ◽  
General Construction ◽  
Special Cases ◽  
Infinite Case ◽  
Standard Wreath Product

AbstractOre (1942) studied the automorphisms of finite monomial groups and Holmes (1956, pp. 23–93) has given the form of the automorphisms of the restricted monomial groups in the infinite case. The automorphism group of a standard wreath product has been studied by Houghton (1962) and Segal (1973, Chapter 4). Monomial groups and standard wreath products are both special cases of permutational wreath product. Here we investigate the automorphisms of the permutational wreath product and consider to what extent the results holding in the special cases remain true for the general construction. Our results extend those of Bunt (1968).

scholarly journals The efficiency of standard wreath product

2000 ◽  
Vol 43 (2) ◽  
pp. 415-423 ◽  
Author(s):  
A. Sinan Çevik
Keyword(s):  
Wreath Product ◽  
Finite Groups ◽  
Sufficient Conditions ◽  
Standard Wreath Product

AbstractLet ξ be the set of all finite groups that have efficient presentations. In this paper we give sufficient conditions for the standard wreath product of two ξ-groups to be a ξ-group.

scholarly journals Topological wreath products

1965 ◽  
Vol 5 (3) ◽  
pp. 396-400 ◽  
Author(s):  
A. Lakshmi
Keyword(s):  
Wreath Product ◽  
Continuous Mapping ◽  
Wreath Products ◽  
Topological Groups ◽  
Locally Compact ◽  
Standard Wreath Product ◽  
Locally Compact Topological Groups ◽  
Product Of Groups

The object of this note is to show that under suitable restrictions some results on the wreath product of groups can be carried over to topological groups. We prove in particular the following analogue of the well-known theorem of Krasner and Kaloujnine (see for example [2] Theorem 3.5): Theorem. Let A and B be two locally compact topological groups, and let (C, ε) be an extension of A by B. If there exists a continuous left inverseof ε, that is to say a continuous mapping τ: B → C such that re is the identity on B, then there exists a continuous monomorphism of C into the topological standard wreath product of A by B.

scholarly journals On Property (FA) for wreath products

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Yves Cornulier ◽  
Aditi Kar
Keyword(s):  
Wreath Product ◽  
Wreath Products ◽  
Standard Wreath Product

AbstractWe characterize permutational wreath products with Property (FA). For instance, we show that the standard wreath product

scholarly journals Embedding inverse semigroups in wreath products

1976 ◽  
Vol 17 (2) ◽  
pp. 77-82 ◽  
Author(s):  
C. H. Houghton
Keyword(s):  
Inverse Semigroup ◽  
Wreath Product ◽  
Inverse Image ◽  
Wreath Products ◽  
Single Component ◽  
Inverse Semigroups ◽  
Component Group ◽  
Previous Condition ◽  
Standard Wreath Product

Any extension of a group A by a group B can be embedded in their wreath product A Wr B. Here we consider generalizations of this result for inverse semigroups.Suppose S is an inverse semigroup and ρ0 is a congruence on S. We put T = S/ρ0 and denote the natural map from S to T by ρ. The kernel of ρ is the inverse image ETρ−1 of the semilattice ET of idempotents of T. First we show that if each ρ0-class of idempotents of S is inversely well-ordered, then S can be embedded in K Wr T, the standard wreath product of K and T. In general, not all elements of K Wr T have inverses. However, we can define a wreath product W(K, T) which is an inverse semigroup and which contains S when the previous condition holds. If ρ0 is idempotent-separating and S is 0-bisimple, K is the union of zero and a family of isomorphic groups. In this case, we can replace K by a single component group G of K, augmented by zero, and show that S can be embedded in W(G0, T). These results are analogous to the extension theories of D'Alarcao [1] and Munn [3] and they give conditions under which all inverse semigroup extensions of an inverse semigroup A by an inverse semigroup T are contained in a semigroup with structure depending only on A and T.

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.

scholarly journals WREATH PRODUCTS, NILPOTENT ORBITS AND SYMPLECTIC DEFORMATIONS

2007 ◽  
Vol 18 (05) ◽  
pp. 473-481
Author(s):  
BAOHUA FU
Keyword(s):  
Wreath Product ◽  
Wreath Products ◽  
Nilpotent Orbit ◽  
Nilpotent Orbits ◽  
Symplectic Resolutions

We recover the wreath product X ≔ Sym 2(ℂ2/± 1) as a transversal slice to a nilpotent orbit in 𝔰𝔭6. By using deformations of Springer resolutions, we construct a symplectic deformation of symplectic resolutions of X.

Commutator Calculus for Wreath Product Groups

2015 ◽  
Vol 43 (5) ◽  
pp. 2152-2173
Author(s):  
Jeffrey M. Riedl
Keyword(s):  
Wreath Product
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