The spectrum of a graph is the set of eigenvalues of its adjacency matrix. A group, together with a multiset of elements of the group, gives a Cayley graph, and a semidirect product provides a method of producing new groups. This paper compares the spectra of cyclic groups to those of their semidirect products, when the products exist. It was found that many of the interesting identities that r...

Let m be a positive integer and let ? finite set. The m-closure of G ? Sym(?) is the largest permutation group G(m) on having same orbits as in its induced action Cartesian product ?m. An exact formula for wreath given. As corollary, sufficient condition obtained this to included m-closures factors.

In the structure theory of inverse semigroups, there are two approaches, basically from the 1970’s, to build up inverse semigroups from semilattices and groups via their semidirect products. These approaches are dual to each other in the sense that one produces any inverse semigroup from a semidirect product of a semilattice by a group by taking an idempotent separating homomorphic image of an ...

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 ...