For finite p-groups where γ_r(G) is 2-generator, γ_r(G) consists only of γ_r-values without the abelian assumption, for all primes p including 3, and the analogous statement holds for pro-p groups.
Blackburn, On prime-power groups in which the derived group has two generators, Proc
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Lower central words in finite $p$-groups
For finite p-groups where γ_r(G) is 2-generator, γ_r(G) consists only of γ_r-values without the abelian assumption, for all primes p including 3, and the analogous statement holds for pro-p groups.