Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-15T19:42:44.831Z Has data issue: false hasContentIssue false
  • English
  • Français

Hypertypes of torsion-free abelian groups of finite rank

Published online by Cambridge University Press:  17 April 2009

H.P. Goeters ,
C. Vinsonhaler  and
W. Wickless
H.P. Goeters
Affiliation:
Mathematics ACA, Auburn University, Auburn, AL 36849, United States of America
C. Vinsonhaler
Affiliation:
Department of Mathematics, University of Connecticut, 196 Auditorium Rd, Storrs, CT. 06268, United States of America
W. Wickless
Affiliation:
Department of Mathematics, University of Connecticut, 196 Auditorium Rd, Storrs, CT. 06268, United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a torsion-free abelian group of finite rank n and let F be a full free subgroup of G. Then G/F is isomorphic to T1 ⊕ … ⊕ Tn, where T1 ⊆ T2 ⊆ … ⊆ Tn ⊆ ℚ/ℤ. It is well known that type T1 = inner type G and type Tn = outer type G. In this note we give two characterisations of type Ti for 1 < i < n.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 21 - 24
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Arnold, D., Finite Rank Torsion Free Abelian Groups and Rings: Lecture Notes in Math. 931 (Springer-Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[2]Fuchs, L., ‘Recent results and problems on Abelian groups’, in Topics in Abelian Groups, pp. 9–40 (Scott and Foresman, Chicago, Illinois, 1963).Google Scholar
[3]Goeters, H.P. and Wickless, W., ‘Hyper-T groups’, Comm. Algebra (to appear).Google Scholar
[4]Richman, F., ‘A class of rank-2 torsion free groups’, Studies on Abelian Groups (B. Charles, Dunod, 1968), 327–333.Google Scholar
[5]Warfield, R., ‘Homomorphisms and duality for torsion free groups’, Math. Z. 107 (1968), 189–200.CrossRefGoogle Scholar