a celebrated result of i. schur asserts that the derived subgroup of a group is finite provided the group modulo its center is finite, a result that has been the source of many investigations within the theory of groups. in this paper we exhibit a similar result to schur's theorem for vector spaces, acted upon by certain groups. the proof of this analogous result depends on the characteristic o...

To each partition λ = (λ1, λ2, . . .) with distinct parts we assign the probability Qλ(x)Pλ(y)/Z where Qλ and Pλ are the SchurQ-functions and Z is a normalization constant. This measure, which we call the shifted Schur measure, is analogous to the much-studied Schur measure. For the specialization of the first m coordinates of x and the first n coordinates of y equal to α (0 < α < 1) and the re...

The theorem in question asserts that, if n > k, then, in the set of integers n, n+1, n-J-2, . . ., n +k-1, there is a number containing a prime divisor greater than k . If n = k+ 1, we obtain the well-known theorem of Chebyshev . The theorem was first asserted and proved by Sylvester t about forty-five years ago . Recently Schurt has rediscovered and again proved the theorem . The following pro...

In a paper [1] published in 2001, we modified a famous theorem of Issai Schur, which asserts that if G is a group with center Z, such that G/Z is finite, then the commutator subgroup G′ = [G,G] is also finite. Our modification was twofold; in the first place, we confined ourselves to nilpotent groups G, so that we could use effective localization methods at an arbitrary family P of primes, and,...

We study classes of filters F on N such that weak and strong F -convergence of sequences in l1 coincide. We study also analogue of l1 weak sequential completeness theorem for filter convergence.

Schur's theorem and its generalisation, Baer's theorem, are distinguished results in group theory, connecting the upper central quotients with lower series. The aim of this paper is to generalise these two different directions, using novel methods related non-abelian tensor product. In particular, we prove a version Schur–Baer for finitely generated groups. Then, apply newly obtained describe k...

Schur studied limits of the arithmetic means An of zeros for polynomials of degree n with integer coefficients and simple zeros in the closed unit disk. If the leading coefficients are bounded, Schur proved that lim supn→∞ |An| ≤ 1 − √ e/2. We show that An → 0, and estimate the rate of convergence by generalizing the Erdős-Turán theorem on the distribution of zeros. As an application, we show t...