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# isomorphism concepts question, eg periods of elliptic functions watch

1. Hi, I have the following:

Let be a discrete subgroup of , the complex plane.

If: i) , then is isomorphic to .

ii) where , then is isomorphic to x

So from what I understand isomorphic is a map that is one to one between two sets that preserves the binary relatione exisising between elements, that is (1), where is the operation the map is isomorphic to.

So to define a isomorphism you need to define: - two sets - the map between them - the relevant operation which is preserved, defined by (1)

QUESTION 1)
So, my book doens't say which operation, is it addition, it also doesn't say which map - is the map to take the integer with the map in case i) and in case 2, under the operation addition it is then easy to show that (1) is obeyed in both cases?

QUESTION 2)
By the wording it seems to imply the fact that is significant for there to be an isomorphism to x, I don't at all understand why, can someone explain? Many thanks in advance
2. apologies i now know the answer.
could a moderator close it or?
ta.

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