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An expression for the number of subgroups of a given order of a finite p-group

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Abstract

We find an exact expression for the number of subgroups of any (possible) order of an arbitrary finite p-group.

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Literature cited

  1. Yu. Shmidt, Selected Works [in Russian], Matematika, Moscow (1959).

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  2. B. Huppert, Endliche Gruppe, Vol. 1, Berlin-Heidelberg-New York (1967).

  3. P. Hall, “A contribution to the theory of groups of prime-power order,” Proc. London Math. Soc.,36, 29–95 (1933).

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Authors and Affiliations

  1. Kabardino-Balkarsk State University, USSR

    V. N. Shokuev

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  1. V. N. Shokuev
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 561–568, November, 1972.

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Shokuev, V.N. An expression for the number of subgroups of a given order of a finite p-group. Mathematical Notes of the Academy of Sciences of the USSR 12, 774–778 (1972). https://doi.org/10.1007/BF01099063

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  • DOI: https://doi.org/10.1007/BF01099063

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