Math Help - Isomorphic groups

1. Isomorphic groups

Let f: G --> H be an isomorphism, G and H are groups.
I've already showed that for every x in G, |f(x)| = |x|. (|x| = order of x, the smallest positive integer such that $x^n$ is the identity element)

How to show that any two isomorphic groups have the same number of elements of n, where n is any positive integer?

2. If two groups are isomorphic, then they have the same cardinality. In order to show that two groups are isomorphic, you must display the isomorphism, that is, the conversion chart that shows how the elements of one group "translate" to the elements of the other group, and that every group operation checks out. Simply by listing the elements of each group, you can show that the groups have the same cardinality. It is also not difficult to show that both groups have an infinite number of members, if that is indeed the case.

3. Originally Posted by dori1123
How to show that any two isomorphic groups have the same number of elements of n, where n is any positive integer?
Because if two groups are isomorphic there is a bijection between them. Therefore, if one group has n elements the other must automatically have n elements because of the bijection.