On Free Products of Torsion Free Abelian Groups

Abstract

Let G be a group. For x,y epsilon G the commutator of x and y is (x, y) = x to the minus 1st power y to the minus 1st power x y. The lower central series of G is a sequence of normal subgroups of G defined inductively as follows: G sub 1 = G, and having defined G sub n (for n a positive integar), G sub n+1 is defined as the group generated by all commutators of (x,y) where x epsilon Gn and y epsilon G. In this paper the lower central series is studied for a group J which is a free product of a finite number of torsion free Abelian groups. In particular, the quotient groups J sub n / Jn sub n+1 are completely determined.

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Document Details

Document Type
Technical Report
Publication Date
Feb 23, 1990
Accession Number
ADA218146

Entities

People

  • A. M. Gaglione

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Availability
  • Biometric Security
  • Classification
  • Commutators
  • Equations
  • Generators
  • Groups (Mathematics)
  • Identification
  • Identification Systems
  • Identities
  • Mathematics
  • Military Research
  • Notation
  • Security
  • United States Naval Academy

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.
  • Linear Algebra