Geodesic
On the dimensions of commutative subalgebras and subgroups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 143-157 
M. V. Milentyeva. On the dimensions of commutative subalgebras and subgroups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 143-157. http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a9/
@article{FPM_2006_12_2_a9,
     author = {M. V. Milentyeva},
     title = {On the dimensions of commutative subalgebras and subgroups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {143--157},
     year = {2006},
     volume = {12},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a9/}
}
TY  - JOUR
AU  - M. V. Milentyeva
TI  - On the dimensions of commutative subalgebras and subgroups
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2006
SP  - 143
EP  - 157
VL  - 12
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a9/
LA  - ru
ID  - FPM_2006_12_2_a9
ER  - 
%0 Journal Article
%A M. V. Milentyeva
%T On the dimensions of commutative subalgebras and subgroups
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2006
%P 143-157
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a9/
%G ru
%F FPM_2006_12_2_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the functions that bound the dimensions of finite-dimensional associative or Lie algebras in terms of the dimensions of their commutative subalgebras. It is proved that these functions have quadratic growth. As a result, we get similar estimates for the dimension of a Lie group with bounded dimensions of its Abelian Lie subgroups.

[1] Burbaki N., Gruppy i algebry Li, Mir, M., 1976 | MR

[2] Vinberg E. B., Onischik A. L., Seminar po gruppam Li i algebraicheskim gruppam, URSS, M., 1995 | MR | Zbl

[3] Maltsev A. I., “Kommutativnye podalgebry poluprostykh algebr Li”, Izv. AN SSSR. Ser. mat., 9:4 (1945), 291–300 | MR | Zbl

[4] Olshanskii A. Yu., “K voprosu o chisle porozhdayuschikh i poryadkakh abelevykh podgrupp konechnykh $p$-grupp”, Mat. zametki, 23 (1978), 3

[5] Skornyakov L. A., Elementy obschei algebry, Nauka, M., 1983 | MR | Zbl

[6] Kherstein I., Nekommutativnye koltsa, Mir, M., 1972 | MR

[7] Milenteva M. V., “On the torsion-free ranks of finitely generated nilpotent groups and of their Abelian subgroups”, J. Group Theory, 7:3 (2004), 403–408 | DOI | MR | Zbl