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Dear experts,

I am looking for two facts about free pro-$p$ groups, and will be glad to receive some reference or suggestions

For convenience reasons, I'll post my questions in two different messages:

In "The structure of groups of prime power order"/Leedham-Green , it is written that there is a normal form of writing the elements in a free pro-$p$ group as a product of basic commutators. Although I am familiar with the collection process in finite groups, I can't understand what is this "normal" form in the free pro-$p$ context.

Does someone have an idea? Can someone tell me where can I find this "normal" form?

Thanks !!!!!

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5  
goodreads.com/quotes/… ;) –  Yemon Choi Nov 23 '12 at 21:19
    
I haven't looked at the paper, but you can write any element in a profinite group as a sequence of elements in finite group quotients which are compatible. Since finite p-groups are nilpotent, one gets a filtration by the lower central p-series. So any element can be expressed as an infinite product of commutators, where the kth element lies in the lower p-central series of the k+1st finite p-group. –  Ian Agol Nov 24 '12 at 7:08
    
OK... Thanks @Agol ! –  Jeremy Young Nov 24 '12 at 9:16

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