In this paper we prove that if V is a vector space over a field of positive characteristric p ≠ 5 then any regular subgroup A of exponent 5 of GL(V) is cyclic. As a consequence a conjecture of Gupta and Mazurov is proved to be true.

Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we might ask that algebraic numbers of a given degree have periodic expansions, just as quadratic irrationals have periodic continued fractions; or we might ask that familiar transcendental constants such as e or π have periodic or terminating expansions. In this paper, we show that there exist such generalized continued function expansions with essentially any desired behaviour.

The two-sided ideals of group near-rings are characterized and studied. Various examples are presented to illustrate the interplay between ideals in the base near-ring R and the corresponding group near-ring R[G]. Some results concerning the Jacobson radicals of R[G] are also discussed.

We give algebraic proofs of some results of Wang on homomorphisms of nonzero degree between aspherical closed orientable 3-manifolds. Our arguments apply to PDn-groups which are virtually poly-Z or have a Kropholler decomposition into parts of generalized Seifert type, for all n.

In this paper we continue to modify and expand a technique due to Enflo for producing nontrivial hyperinvariant subspaces for quasinilpotent operators, and thereby obtain such subspaces for some additional quasinilpotent operators on Hilbert space. We also obtain a structure theorem for a certain class of operators.

A Banach space (X, ∥ · ∥) is said to be a dual differentiation space if every continuous convex function defined on a non-empty open convex subset A of X* that possesses weak* continuous subgradients at the points of a residual subset of A is Fréchet differentiable on a dense subset of A. In this paper we show that if we assume the continuum hypothesis then there exists a dual differentiation space that does not admit an equivalent locally uniformly rotund norm.

This note improves two previous results of the second author. They turn out to be special cases of our main theorem which states: A Banach space X has the property that the strong closure of every abstractly σ-complete Boolean algebra of projections in X is Bade complete if and only if X does not contain a copy of the sequence space ℓ∞.

In this paper, we give a generalization of Hardy's theorems for the Dunkl transform ℱD on ℝd. More precisely for all a > 0, b > 0 and p, q ∈ [1, + ∞], we determine the measurable functions f on ℝd such that where are the Lebesgue spaces associated with the Dunkl transform.

Let G be a finite p-solvable group for a fixed prime p. We study how certain arithmetical conditions on the set of p-regular conjugacy class sizes of G influence the p-structure of G. In particular, the structure of the p-complements of G is described when this set is {1, m, n} for arbitrary coprime integers m, n > 1. The structure of G is determined when the noncentral p-regular class lengths are consecutive numbers and when all of them are prime powers.

Let K be a field of prime characteristic p and let G be a finite group with a Sylow p-subgroup of order p. For any finite-dimensional K G-module V and any positive integer n, let Ln (V) denote the nth homogeneous component of the free Lie K-algebra generated by (a basis of) V. Then Ln(V) can be considered as a K G-module, called the nth Lie power of V. The main result of the paper is a formula which describes the module structure of Ln(V) up to isomorphism.

In this paper we study the pseudorandom properties of the signs of Kloosterman sums.