Balanced and Cobalanced Butler Groups

✍ Scribed by K.Peter Krog

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 157 KB
• Volume: 238
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8669

✦ Synopsis

The class of Butler groupsᎏpure subgroups of finite-rank torsion-free completely decomposable groupsᎏhas been widely studied by abelian group theorists.

Here we present several classification results for groups in two chains of special Ž . Ž . Ž . subclasses of the Butler groups, the K K n -and co-K K n -groups. The classes K K n Ž . and co-K K n , n G 1, are defined by balanced and cobalanced exact sequences of Butler groups, respectively. We give direct sum decompositions of certain pure Ž . Ž . subgroups of K K n -groups and certain torsion-free quotients of co-K K n -groups. The direct sum decompositions characterize the groups in those classes and extend some well-known results for Butler groups.