Proving Isomorphism of Z4 / (2Z4) to Z2

[Dawson64]

Why does it make sense ( when considering Z₄)to form the factor group

Z₄ / (2Z₄) where kZ_n = {0, k mod n, 2k mod n, ..., nk mod n}?

I believe that this above factor group is isomorphic to Z₂, but how can I prove this?

 

[Newtime]

Why does it make sense ( when considering Z₄)to form the factor group

Z₄ / (2Z₄) where kZ_n = {0, k mod n, 2k mod n, ..., nk mod n}?

I believe that this above factor group is isomorphic to Z₂, but how can I prove this?

The groups you're considering are of very small order so in this case, just write out the elements and remember the number of groups of order 2 is ______ . In general, based off your definition, you should be able to identify the group pretty easily by what you know about finite cyclic groups.