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Philip Hall's ‘rather curious’ formula for abelianp-groups

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Abstract

We provide a new proof for a formula of Philip Hall concerning the orders of finite abelian groups.

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References

  • [Ha36] P. Hall,The Eulerian functions of a group, The Quarterly Journal of Mathematics, Oxford7 (1936), 134–151.

    Article  Google Scholar 

  • [Ha38] P. Hall,A partition formula connected with Abelian groups, Commentarii Mathematici Helvetici11 (1938), 126–129.

    Article  MathSciNet  Google Scholar 

  • [HW] G. H. Hardy and E. M. Wright,An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, 1979.

  • [Lu93] A. Lubotzky,Subgroup growth, Lecture Notes, University College, Galway, 1993.

    Google Scholar 

  • [Lu95] A. Lubotzky,Counting finite index subgroups, inGroups '93 Galway/St Andrews, Cambridge University Press, 1995, pp. 368–404.

  • [Ma] A. Mann,Positively finitely generated groups, Forum Mathematicum8 (1996), 429–459.

    Article  MATH  MathSciNet  Google Scholar 

  • [Mc] I. G. Macdonald,The algebra of partitions, inGroup Theory: Essays for Philip Hall, Academic Press, London, 1984, pp. 315–333.

    Google Scholar 

  • [MS] A. Mann and D. Segal,Subgroup growth: some current developments, inInfinite Groups 94, de Gruyter, Berlin, 1995, pp. 179–197.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904, Jerusalem, Israel

    Avinoam Mann

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  1. Avinoam Mann
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Correspondence to Avinoam Mann.

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To the memory of my great teacher and friend, Shimshon Amitsur

The author is grateful to John Thompson for first drawing his attention to Hall's theorem, to Hershel Farkas for stimulating conversations on the subject of partitions, and to Marta Morigi for pointing out inaccuracies in an earlier version of this note.

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Mann, A. Philip Hall's ‘rather curious’ formula for abelianp-groups. Israel J. Math. 96, 445–448 (1996). https://doi.org/10.1007/BF02937316

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  • DOI: https://doi.org/10.1007/BF02937316

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