Geodesic
On the dimensions of commutative subalgebras and subgroups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 143-157

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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. 
@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},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a9/}
}
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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/