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2 votes

Local vs global nilpotence class (Lazard correspondence)

This is not a complete answer (only gives the answer for p=2,3,5) but it is also too long to add as a comment! Known results concerning similar questions as yours suggest that the nilpotency class of …
Alireza Abdollahi's user avatar
5 votes

Quotients of finitely generated nilpotent groups

I answer the edited question. Every finitely generated nilpotent group contains a torsion-free subgroup of finite index (even better a poly-(infinite cyclic) subgroup). See Proposition 2 in page 2 of …
Alireza Abdollahi's user avatar