Question

give a example of infinite group or non proper subgroups are infinite​

Answer 1

Answer:

In conclusion: Zp∞ is an infinite group whose proper subgroups are all finite. It is a non-cyclic group whose all proper subgroups are cyclic.

Answer 2

Answer:

We study some properties of the Prüfer p-group Zp∞ for a prime number p. The Prüfer p-group may be identified with the subgroup of the circle group, consisting of all pn-th roots of unity as n ranges over all non-negative integers:

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