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

[charlamov]

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 $Z_{p^ \infinity}$

 

[DonAntonio]

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

 

[micromass]

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