Bulletin of the Australian Mathematical Society

Research Article

SELF-SMALL ABELIAN GROUPS

ULRICH ALBRECHTa1 c1, SIMION BREAZa2 and WILLIAM WICKLESSa3

a1 Department of Mathematics, Auburn University, Auburn, AL 36849, USA (email: albreuf@mail.auburn.edu)

a2 ‘Babeş-Bolyai’ University, Faculty of Mathematics and Computer Science, Str. Mihail Kogălniceanu 1, 400084 Cluj-Napoca, Romania (email: bodo@math.ubbcluj.ro)

a3 Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA (email: wickless@math.uconn.edu)

Abstract

This paper investigates self-small abelian groups of finite torsion-free rank. We obtain a new characterization of infinite self-small groups. In addition, self-small groups of torsion-free rank 1 and their finite direct sums are discussed.

(Received October 23 2008)

2000 Mathematics subject classification

  • primary 20K21

Keywords and phrases

  • self-small group;
  • projection condition;
  • essentially W-reduced group

Correspondence:

c1 For correspondence; e-mail: albreuf@mail.auburn.edu

Footnotes

The second author is supported by grant no. PN2CD ID-489.