Let $F$ be a free group and let $V$ be another verbal subgroup of $F$ such that $$ F = [F,F] V. $$ Is it true that $V=F?$ More generally, if $N$ is a normal (or even characteristic) subgroup of $F$ which also supplements $[F,F],$ $$ F=[F,F] N $$ is it true that $N=F?$
2026-02-23 05:42:20.1771825340
Free groups: normal supplements of the commutator subgroup
135 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in GROUP-THEORY
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