We give several new applications of the wreath product of forest algebras to the study of logics on trees. These include new simplified proofs of necessary conditions for definability in CTL and first-order logic with the ancestor relation; a sequence of identities satisfied by all forest languages definable in PDL; and new examples of languages outsideCTL, along with an application to the ques...

We propose the use of spectral analysis on certain noncommutative finite groups in digital signal processing, and in particular, image processing. We pay significant attention to groups constructed as wreath products of cyclic groups. Within this large class of groups our approach recovers the DFT, Haar wavelet transform, various multichannel pyramid filter banks and other aspects of multiresol...

We additionally obtain a complete characterization of inner amenability for permutational wreath product groups. One the main ingredients used this is general lemma which we call location lemma, allows us to “locate” conjugation invariant means on group $G$ relative given normal subgroup $N$ $G$. give several further applications beyond aforementioned amenable products.

We give a geometric proof based on recent work of Eskin, Fisher and Whyte that the lamplighter group Ln has infinitely many twisted conjugacy classes for any automorphism φ only when n is divisible by 2 or 3, originally proved by Gonçalves and Wong. We determine when the wreath product G o Z has this same property for several classes of finite groups G, including symmetric groups and some nilpo...

If in a transformation semigroup we assume that the set being acted upon has a semigroup structure, then the transformation semigroup can be used to recognize languages of unranked trees. This observation allows us to examine the relationship connecting languages of unranked trees with standard algebraic concepts such as aperiodicity, idempotency, commutativity and wreath product. In particular...

In this paper we define a particular Markov chain on some combinatorial structures called orthogonal block structures. These structures include, as a particular case, the poset block structures, which can be naturally regarded as the set on which the generalized wreath product of permutation groups acts as the group of automorphisms. In this case, we study the associated Gelfand pairs together ...

[10] proposed a generative theory of shape, and general cognition, based on group actions on sets as defined by the wreath product. Our position expressed here is that this approach can provide a strong basis for robot cognition when: 1. tightly coupled to sensorimotor data and analysis, 2. used to structure both general concepts and specific instances, and 3. combined with a probabilistic fram...

Let K be field of characteristic 2 and let G be a finite nonabelian 2-group with the cyclic derived subgroup G′, and there exists a central element z of order 2 in Z(G)\G′. We prove that the unit group of the group algebra KG possesses a section isomorphic to the wreath product of a group of order 2 with the derived subgroup of the group G, giving for such groups a positive answer to the questi...

We define and study a notion of free wreath product with amalgamation for compact quantum groups. These objects were already introduced in the case duals discrete groups under name “free products pairs” previous work ours. give several equivalent descriptions use them to establish properties like residual finiteness, Haagerup property or smash decomposition.

The framework of C-varieties, introduced by the third author, extends the scope of Eilenberg’s variety theory to new classes of languages. In this paper, we first define C-varieties of actions, which are closely related to automata, and prove their equivalence with the original definition of C-varieties of stamps. Next, we complete the study of the wreath product initiated by Ésik and Ito by ex...