The discussion centers on proving that the group presentation < 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 > represents the Prüfer group Z_{p^\infty}. Participants emphasize the necessity of defining the Prüfer group clearly to facilitate understanding and proof. DonAntonio Charlamov is encouraged to share previous attempts to provide context for further assistance.
PREREQUISITESMathematicians, particularly those specializing in group theory, algebra students, and anyone interested in the properties and proofs related to the Prüfer group Z_{p^\infty}.
charlamov said:How would you prove that [itex]< 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 >[/itex] is presentation of [itex]Z_{p^ \infinity}[/itex]