Geodesic
On ranks of elements of free groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 313-315.

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A criterion for a system of elements of the free group to have given rank is obtained. This result is a group analog of the theorem of A. A. Mikhalev and A. A. Zolotykh on ranks of system of elements in free Lie algebras. 
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     author = {U. U. Umirbaev},
     title = {On ranks of elements of free groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     volume = {2},
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     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a20/}
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U. U. Umirbaev. On ranks of elements of free groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 313-315. http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a20/