An algebraic proof that pseudovarieties are defined by pseudoidentities

An algebraic proof is given which shows that any pseudovariety of finite algebras is determined by a set of pseudoidentities.Presented by Boris M. Schein.     

On braid groups

A dissertation in the Department of Mathematics submitted to the Faculty of the Graduate School of Arts and Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at New York University.     

The constructive theory of torsion-free abelian groups

The theory of torsion-free abelian groups is developed, in a manner that is constructive in the sense of Bishop, up to the fundamental the orem that, for finite-rank completely decomposable torsion-free groups, the class of finite-rank pure subgroups is coextensive with the class of finite-rank torsion-free quotients.     

The arithmetical hierarchy of nilpotent torsion-free groups

Previously, N. Khisamiev proved that all {ie172-1} Abelian torsion-free groups are {ie172-2}. We prove that for the class of nilpotent torsion-free groups, the situation is different: even the quotient group F of a {ie172-3} nilpotent group of class 2 by its periodic part may fail to have a {ie172-4}. Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 308–313, May–June, 1996.     

Galois rigidity of pro- pure braid groups of algebraic curves

In this paper, Grothendieck's anabelian conjecture on the pro- fundamental groups of configuration spaces of hyperbolic curves is reduced to the conjecture on those of single hyperbolic curves. This is done by estimating effectively the Galois equivariant automorphism group of the pro- braid group on the curve. The process of the proof involves the complete determination of the groups of graded automorphisms of the graded Lie algebras associated to the weight filtration of the braid groups on Riemann surfaces.

     

Fully transitive torsion-free Abelian groups

Translated from Algebra i Logika, Vol. 29, No. 5, pp. 549–560, September–October, 1990.