Wreath products of ordered semigroups

In this paper ordered wreath products of ordered monoids by ordered acts are investigated. In 4. we characterize idempotent isotone wreath products. In 3. the monoid of order preserving endomorphisms of a free ordered act is represented as Cartesian ordered isotone wreath product. Moreover, we give conditions for this wreath product to be I-regular.     

Semidirect products and wreath products of strongly π-inverse monoids

In this paper we determine the necessary and sufficient conditions for the semidirect products and the wreath products of two monoids to be strongly -inverse. Furthermore, we determine the least group congruence on a strongly -inverse monoid, and we give some important isomorphism theorems.     

A torsion—theoretic generalization of fully bounded Noetherian rings

ABSTRACT

We introduce semidirect and wreath products of finite ordered semigroups and extend some standard decomposition results to this case.     

Reflection functors and symplectic reflection algebras for wreath products

We construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver. These functors give equivalences of categories associated to generic parameters which are in the same orbit under the Weyl group action. We give applications to the representation theory of symplectic reflection algebras of wreath product groups.     

On semidirect products and wreath products of partially ordered groups

The notions of Cartesian and semidirect products for partially ordered groups are considered. A series of results on those products of AO \mathcal{A}\mathcal{O} -groups and interpolation groups is obtained. Some results concerning wreath products of directed groups are obtained.     

Terwilliger algebras of wreath products by quasi-thin schemes

The structure of Terwilliger algebras of wreath products by thin schemes or one-class schemes was studied in [A. Hanaki, K. Kim, Y. Maekawa, Terwilliger algebras of direct and wreath products of association schemes, J. Algebra 343 (2011) 195–200]. In this paper, we will consider the structure of Terwilliger algebras of wreath products by quasi-thin schemes. This gives a generalization of their result.     

Product action

This paper studies the cycle indices of products of permutation groups. The main focus is on the product action of the direct product of permutation groups. The number of orbits of the product on n-tuples is trivial to compute from the numbers of orbits of the factors; on the other hand, computing the cycle index of the product is more intricate. Reconciling the two computations leads to some interesting questions about formal power series. We also discuss what happens for infinite (oligomorphic) groups and give detailed examples. Finally, we briefly turn our attention to generalised wreath products, which are a common generalisation of both the direct product with the product action and the wreath product with the imprimitive action.     

Integral Reverse Estimates for Logarithmic Bloch Spaces in the Ball

In this note, we focus again on the basics of triangular product of automata construction and to introduce the notion of linear automata complexity. It contains three main results. (1) For any two pure automata we consider the category of their cascade connections. It possesses the universal terminal object. This object is the wreath product of the automata. Hence, every cascade connection admits a natural embedding into the wreath product of automata. (2) A similar theory is developed for linear automata, where we also consider the category of cascade connections. It also has the terminal object. This object is the triangular product of linear automata. (3) Triangular products have various applications. This construction is used in linear automata decomposition theory and in the definition of complexity of a linear automaton. We consider a special linear complexity and give the rule for its calculation.     

Three types of inclusions of innately transitive permutation groups into wreath products in product action

A permutation group is innately transitive if it has a transitive minimal normal subgroup, and this subgroup is called a plinth. In this paper we study three special types of inclusions of innately transitive permutation groups in wreath products in product action. This is achieved by studying the natural Cartesian decomposition of the underlying set that corresponds to the product action of the wreath product. Previously we identified six classes of Cartesian decompositions that can be acted upon transitively by an innately transitive group with a non-abelian plinth. The inclusions studied in this paper correspond to three of the six classes. We find that in each case the isomorphism type of the acting group is restricted, and some interesting combinatorial structures are left invariant. We also give a fairly general construction of inclusions for each type.     

On a multiplication of semigroup varieties

The role of multiplication of group varieties is well known [2], as well as the role of wreath products in such a construction [1]. In the present paper the idea of exploiting wreath products is used for defining a multiplication for semigroup varieties which differs from the operations given in [3]. In section 5 we also consider some elementary properties of the defined multiplication. Some results of the paper were announced in [9].     

Reaching the minimum ideal in a finite semigroup

We introduce the depth parameters of a finite semigroup, which measure how hard it is to produce an element in the minimum ideal when we consider generating sets satisfying some minimality conditions. We estimate such parameters for some families of finite semigroups, and we obtain an upper bound for wreath products and direct products of two finite (transformation) monoids.     

On self-adjoint subloops of moufang loops

In this paper we give a combinatorial rule to compute the composition of two convolution products of endomorphisms of a free associative algebra and deduce the construction of a subalgebra of QB _n (the group algebra of Hyperoctahedral group) which contains the descent algebra X#?. We also deduce a proof of the multiplication rule in the algebra ∑QB _n- Finally, we generalize this construction to other wreath products of symmetric groups by abelian groups.     

Generalized involution models for wreath products

We prove that if a finite group H has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product H ? S _n also has a generalized involution model. This extends the work of Baddeley concerning involution models for wreath products. As an application, we construct a Gel’fand model for wreath products of the form A ? S _n with A abelian, and give an alternate proof of a recent result due to Adin, Postnikov and Roichman describing a particularly elegant Gel’fand model for the wreath product ? _r ? S _n . We conclude by discussing some notable properties of this representation and its decomposition into irreducible constituents, proving a conjecture of Adin, Postnikov and Roichman.     

直觉模糊有限自动机的乘积

给出了直觉模糊有限自动机的广义直积、级联积和圈积及覆盖的定义,讨论了直觉模糊有限自动机在同构意义下级联积和圈积满足结合性以及各种乘积之间的覆盖关系。     

Innately transitive subgroups of wreath products in product action

A permutation group is innately transitive if it has a transitive minimal normal subgroup, which is referred to as a plinth. We study the class of finite, innately transitive permutation groups that can be embedded into wreath products in product action. This investigation is carried out by observing that such a wreath product preserves a natural Cartesian decomposition of the underlying set. Previously we classified the possible embeddings in the case where the plinth is simple. Here we extend that classification and identify several different types of Cartesian decompositions that can be preserved by an innately transitive group with a non-abelian plinth. These different types of decompositions lead to different types of embeddings of the acting group into wreath products in product action. We also obtain a full characterisation of embeddings of innately transitive groups with diagonal type into such wreath products.

     

The probability of generating certain profinite groups by two elements

In this paper we consider the question of finite generation of profinite groups. We study the class of profinite groups which are inverse limits of wreath products of alternating groups of degree ≥5. We prove that the probability of generating such inverse limits by two elements is strictly positive and tends to 1 as the degree of the first factor tends to infinity. Our method of analysis requires a survey of the maximal subgroups of iterated wreath products of alternating groups. Although we have been unable to classify these precisely we do obtain upper bounds for the number of conjugacy classes of maximal subgroups which we believe to be of independent interest. The author is grateful for financial support received under the FCO-award scheme.     

右（左）逆半群的半直积及圈积

给出了两个幺半群的半直积及圈积为右（左）逆半群的充分必要条件，从而推广了[2]中两个幺半群的半幺直积和圈积为逆半群的充分必要条件．