G. P. Egorychev, Yu. D. Ushakov, “The ranks of the <nobr>$p$</nobr>-central series of free groups of certain manifolds”, Mat. Zametki, 1977, Volume 22, Issue 4,Pages <nobr>575

The ranks of the $p$-central series of free groups of certain manifolds

G. P. Egorychev^a, Yu. D. Ushakov^b

^a Institute of Physics, Siberian Branch of USSR Academy of Sciences
^b Krasnoyarsk Polytechnic Institute

Abstract: 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.

UDC: 519.4

Received: 07.07.1976