I am trying to get a clear view of "free nilpotent group". It seems I am not familiar with the use of word free. The word free is also used in other unrelated context, for example "free probability". The link of those basic definition is below:
https://en.wikipedia.org/wiki/Free_probability
https://groupprops.subwiki.org/wiki/Free_nilpotent_group
Is there a common way to interpret the word free? I would like to know what exactly the word free mean in case of Nilponent group?
From comments:
The Wikipedia article Free object gives a category-theoretic description of the usual meaning of "free" in abstract algebra and related fields.