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Enumeration of Certain Subgroups of Abelian p-Groups

Published online by Cambridge University Press:  20 January 2009

I. J. Davies
I. J. Davies
Affiliation:
University College, Swansea
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The number of distinct types of Abelian group of prime-power order pn is equal to the number of partitions of n. Let (ρ) = (ρ1, ρ2, …, ρr) be a partition of n and let (μ) = (μ1, μ2, …, μs) be a partition of m, with ρ1≧ρ2≧…≧ρr and μ1≧μ2≧…≧μs, ρi≧μi, r≧s, n>m. The number of subgroups of type μ in an Abelian p-group of type (ρ) is a function of the two partitions (μ) and p, and has been determined as a polynomial in p with integer coefficients by Yeh (1), Delsarte (2) and Kinosita (3). Their results differ in form but are equivalent.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 1 , June 1962 , pp. 1 - 4
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

REFERENCES

(1) Yeh, Y., On prime power Abelian Groups, Bull. Amer. Math. Soc, 54 (1948),323–327.Google Scholar
(2) Delsarte, S., Fonctions de Möbius sur les groupes abeliens finis. Ann. of Math., (2) 49 (1948), 600–609.Google Scholar
(3) Kinosita, Y., On an enumeration of certain subgroups of a p-group. J. Osaka Inst. Sci. Tech. Part I, 1 (1949), 13–20.Google Scholar
(4) Hall, P., Edinburgh Mathematical Society Colloquium, St Andrews, 1955Google Scholar