Abstract
In this paper we are interested in the relationship of the lower central series of a normal subgroup of finite index to the lower central series of a free group. If F is a free group and S is the subgroup, then clearly S,,, is a subgroup of F,, . Moreover, S,,,, is a characteristic subgroup of S; hence, it is a normal subgroup of F and therefore of F,,,, . The problem to tihich we shall devote our attention is that of saying as much as we can about the structure of the quotient group Fm+l/Sm+l . IftherankofFisOor1,orifSisallofF, then Fm+l~Sm+l is the one element group. The free group of rank 2 is already a wild beast malting life non-trivial for group theorists. Accordingly, our investigations have for ground rules rank(F) 3 2 and (F: S ( > 2.
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