The Peiffer product of groups first arose in work of J.H.C. Whitehead on the structure of relative homotopy groups, and is closely related to problems of asphericity for two-complexes. We develop algebraic methods for computing the second integral homology of a Peiffer product. We show that a Peiffer product of superperfect groups is superperfect, and determine when a Peiffer product of cyclic ...

We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hilbert schemes of points on a surface. Introduction It is by now well known that a direct sum ⊕ n≥0R(Sn) of the Grothendieck rings of symmetric groups Sn can be identified with the Fock space of the Hei...

Straubing’s wreath product principle provides a description of the languages recognized by the wreath product of two monoids. A similar principle for ordered semigroups is given in this paper. Applications to language theory extend standard results of the theory of varieties to positive varieties. They include a characterization of positive locally testable languages and syntactic descriptions ...

We strengthen a classical result of Sabidussi giving a necessary and sufficient condition on two graphs, X and Y , for the automorphsim group of the wreath product of the graphs, Aut(X o Y ) to be the wreath product of the automorphism groups Aut(X) o Aut(Y ). We also generalize this to arrive at a similar condition on color digraphs. The main purpose of this paper is to revisit a well-known an...

Abstract. Let [X/G] be an orbifold which is a global quotient of a compact almost complex manifold X by a finite group G. Let Σn be the symmetric group on n letters. Their semidirect product G ⋊ Σn is called the wreath product of G and it naturally acts on the n-fold product X, yielding the orbifold [X/(G ⋊Σn)]. Let H (X , G ⋊Σn) be the stringy cohomology [FG, JKK1] of the (G ⋊ Σn)-space X . Wh...

Let G be a finite group acting on the finite set X such that the corresponding (complex) permutation representation is multiplicity free. There is a natural rank and order preserving action of the wreath product G ∼ Sn on the generalized Boolean algebra BX(n). We explicitly block diagonalize the commutant of this action.

The wreath product W = A i T, where A ^ 1, is of type FP2 if and only if T is finite and A is of type FP2. 1991 Mathematics subject classification (Amer. Math. Soc): primary 20E22, 20F05, 20J05.

This paper continues the investigation in digital signal processing of spectral analysis on certain non-commutative nite groups|wreath product groups. We describe here the generalization of discrete cyclic convolution to convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group based convolution is deened in both the spatial and spectral domain...

The theory of spectral analysis of a particular class of non-commutative groups|wreath products of cyclic groups| has been shown to have a group-based convolution that leads to a new class of noncommutative lters. These lters, with their group and scale-selective properties and their relationship to DFT lter banks, ooer some intriguing possibilities in signal processing applications. In this pa...