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. 
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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/

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