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AN EXPLICIT FORMULA FOR THE NUMBER OF SUBGROUPS OF A FINITE ABELIAN p-GROUP UP TO RANK 3

  • Oh, Ju-Mok (Department of Mathematics Gangneung-Wonju National University)
  • Received : 2011.10.07
  • Published : 2013.10.31

Abstract

In this paper we give an explicit formula for the total number of subgroups of a finite abelian $p$-group up to rank three.

Keywords

Acknowledgement

Supported by : Gangneung-Wonju National University

References

  1. G. Calugareanu, The total number of subgroups of a finite abelian group, Sci. Math. Jpn. 60 (2004), no. 1, 157-167.
  2. I. J. Davies, Enumeration of certain subgroups of abelian p-groups, Proc. Edinburgh Math. Soc. 13 (1962), no. 2, 1-4. https://doi.org/10.1017/S0013091500014425
  3. S. Delsarte, Fonctions de Mobius sur les groupes abeliens finis, Ann. of Math. 49 (1948), no. 2, 600-609. https://doi.org/10.2307/1969047
  4. P. Dyubyuk, On the number of subgroups of a finite abelian group, Soviet Math. 2 (1961), 298-300.
  5. J. Petrillo, Counting subgroups in a direct product of finite cyclic groups, College Math. J. 42 (2011), no. 3, 215-222. https://doi.org/10.4169/college.math.j.42.3.215
  6. Y. Yeh, On prime power abelian groups, Bull. Amer. Math. Soc. 54 (1948), 323-327. https://doi.org/10.1090/S0002-9904-1948-08995-9

Cited by

  1. -groups pp.1793-7183, 2019, https://doi.org/10.1142/S1793557120500941