I am looking for good, detailed references for "mod $p$ lower central series".

So far I only find papers such as (https://core.ac.uk/download/pdf/81193793.pdf,https://www.sciencedirect.com/science/article/pii/0040938366900243), which briefly mention it in the context of topology.

Are there any good books that discuss this in detail (not necessarily related to topology)?

Also, just to confirm, are these terminologies the same thing:

1. mod $p$ lower central series
2. lower $p$-central series
3. lower exponent-p central series

I am confused by the different terminologies.

Thanks a lot.