Is the Prüfer Group Presentation Proof for Z_{p^\infinity} Possible?

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How would you prove that < x_1,x_2 ... | [ x_i , x_j ] =1, i,j \in N , x_1 ^ p = 1, x_{i+1} ^p = x_i , i \in N > is presentation of Z_{p^ \infinity}
 
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charlamov said:
How would you prove that < x_1,x_2 ... | [ x_i , x_j ] =1, i,j \in N , x_1 ^ p = 1, x_{i+1} ^p = x_i , i \in N > is presentation of Z_{p^ \infinity}



Well, why won't you first tell us what is your definition of the Prüfer group, so that we all will know what's needed to prove?

DonAntonio
 
Charlamov, you first need to show us what you tried before we can help.
 

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