We characterize which permutational wreath products G⋉W (X) are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X. On the one hand, this extends a result of G. Baumslag about infinite presentation of standard wreath products; on the other hand, this provides nont...

Let Xp = Gp/Kp be homogeneous spaces (Kp a compact subgroup of a locally compact group Gp) with dimension parameter p such that the double coset spaces Gp//Kp can be identified with some fixed space X . Then we obtain projections Tp : Xp → X , and for a given probability measure ν ∈ M(X) there exist unique ”radial”, i.e. Kp-invariant measures νp ∈ M1(Xp) with Tp(νp) = ν and associated radial ra...

This paper is a report on work in progress rather than a description of theorems which have attained their final form. The results I shall describe are part of an attempt to continue to higher dimensions the study of the relation between the Hasse-Weil zeta-functions of Shimura varieties and the Euler products associated to automorphic forms, which was initiated by Eichler, and extensively deve...

Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...

A theory for the transitive action of a group on the configuration space of a system of fermions is shown to lead to the conclusion that bosons can be represented by the action of cosets of the group. By application of the principle to fundamental, indivisible fermions, the symplectic group Sp (n) is shown to be the largest group of isometries of the space. Interactions between particles are re...

We study the hardness of the dihedral hidden subgroup problem. It is known that lattice problems reduce to it, and that it reduces to random subset sum with density > 1 and also to quantum sampling subset sum solutions. We examine a decision version of the problem where the question asks whether the hidden subgroup is trivial or order two. The decision problem essentially asks if a given vector...

Our aim is to derive the effective action in four dimensions resulting by reducing dimensionally the ten-dimensional N = 1 heterotic supergravity coupled to N = 1 super Yang-Mills over manifolds admitting a nearly-Kähler structure. Given the fact that all homogeneous six-dimensional nearly-Kähler manifolds are included in the class of the corresponding non-symmetric coset spaces plus a group ma...

Let H and K be subgroups of a group G. The double cosets of H and K in G are the sets HgK, g E G. In this paper we describe a procedure, P, for determining the cardinality of the set H\G/K of double cosets of H and K in G given a finite presentation for G and finite sets of generators for H and K. It is well known that the problem of determining whether or not a group G defined by a finite pres...