Geodesic
The number of generators and orders of Abelian subgroups of finite p-groups
Matematičeskie zametki, Tome 23 (1978) no. 3, pp. 337-341 
A. Yu. Ol'shanskii. The number of generators and orders of Abelian subgroups of finite p-groups. Matematičeskie zametki, Tome 23 (1978) no. 3, pp. 337-341. http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a0/
@article{MZM_1978_23_3_a0,
     author = {A. Yu. Ol'shanskii},
     title = {The number of generators and orders of {Abelian} subgroups of finite p-groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {337--341},
     year = {1978},
     volume = {23},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.