This article is cited in 14 papers

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

A. Yu. Ol'shanskii

M. V. Lomonosov Moscow State University

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 $p^n$, has at most $f(n)$ generators (has order not exceeding $p^{F(n)}$). It is established that the functions $f$ and $F$ have quadratic order of growth.

UDC: 512

Received: 26.10.1976

 English version: Mathematical Notes, 1978, 23:3, 183–185

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