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A Generalization of Final Rank of Primary Abelian Groups

Published online by Cambridge University Press:  20 November 2018

Doyle O. Cutler  and
Paul F. Dubois
Doyle O. Cutler
Affiliation:
University of California, Davis, California
Paul F. Dubois
Affiliation:
University of Alberta, Edmonton, Alberta
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Let G be a p-primary Abelian group. Recall that the final rank of G is infn∈ω{r(pnG)}, where r(pnG) is the rank of pnG and ω is the first limit ordinal. Alternately, if Γ is the set of all basic subgroups of G, we may define the final rank of G by supB∈Γ {r(G/B)}. In fact, it is known that there exists a basic subgroup B of G such that r(G/B) is equal to the final rank of G. Since the final rank of G is equal to the final rank of a high subgroup of G plus the rank of pωG, one could obtain the same information if the definition of final rank were restricted to the class of p-primary Abelian groups of length ω.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 6 , 01 December 1970 , pp. 1118 - 1122
Copyright
Copyright © Canadian Mathematical Society 1970

References

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