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The number of generators and orders of Abelian subgroups of finite p-groups

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Abstract

Let f(F) be the smallest function such that every finite p-group, all of whose Abelian subgroups are generated by at most n elements (all of whose Abelian subgroups have orders at most pn, has at most f(n) generators (has order not exceeding pF(n)). It is established that the functions f and F have quadratic order of growth.

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Literature cited

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. Yu. Ol'shanskii

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  1. A. Yu. Ol'shanskii
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Translated from Matematicheskie Zametki, Vol. 23, No. 3, pp. 337–341, March, 1978.

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Ol'shanskii, A.Y. The number of generators and orders of Abelian subgroups of finite p-groups. Mathematical Notes of the Academy of Sciences of the USSR 23, 183–185 (1978). https://doi.org/10.1007/BF01651428

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  • DOI: https://doi.org/10.1007/BF01651428

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