p-Lower central series, relevance?

Given a group G, the p-lower central series is defined by:

P_0(G)=G;
P_{i+1}(G)=[G,P_i(G)]P_i(G).

Could anyone please tell me the relevance of this subgroups, or a good
reference. I found for example that the automorphism of a finite p-
group can be computed inductively using this groups.

Thanks.

.

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