Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

New criteria for freeness in abelian groups. II


Author: Paul Hill
Journal: Trans. Amer. Math. Soc. 196 (1974), 191-201
MSC: Primary 20K20
MathSciNet review: 0352294
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A new criterion is established for an abelian group to be free. The criterion is in terms of an ascending chain of free subgroups and is dependent upon a new class of torsion-free groups. The result leads to the construction, for each positive integer n, of a group $ {G_n}$ of cardinality $ {\aleph _n}$ that is not free but is $ {\aleph _n}$-free. A conjecture in infinitary logic concerning free abelian groups is also verified.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20K20

Retrieve articles in all journals with MSC: 20K20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0352294-8
PII: S 0002-9947(1974)0352294-8
Keywords: Smooth chain of free groups, $ {\aleph _n}$-free, $ {\beth _n}$-free groups, non-free $ {\aleph _n}$-free groups, equivalence in $ {L_{\infty \kappa }}$
Article copyright: © Copyright 1974 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia