Geodesic
The ranks of the $p$-central series of free groups of certain manifolds
Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 575-582

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A factor basis is found for the $p$-central series of a free torsion-free group for which a factor basis of the lower central series can be chosen among the basis commutators. For free solvable groups of finite rank, recursion formulas are obtained for the calculation of the ranks of the factors of the $p$-central series. 
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     author = {G. P. Egorychev and Yu. D. Ushakov},
     title = {The ranks of the $p$-central series of free groups of certain manifolds},
     journal = {Matemati\v{c}eskie zametki},
     pages = {575--582},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a13/}
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G. P. Egorychev; Yu. D. Ushakov. The ranks of the $p$-central series of free groups of certain manifolds. Matematičeskie zametki, Tome 22 (1977) no. 4, pp. 575-582. http://geodesic.mathdoc.fr/item/MZM_1977_22_4_a13/