I came up with a new group.
Let where .
Then under complex multiplication will form a group.
I hope this is group is not isomorphic to any of the known ones. And hopefully has some interesting properties.
We know the following:
1) is an abelian group.
2) is a countable group.
3*) has a cyclic subgroup for every finite order.
What are the answers to the following questions:
1)Is is free abelian group?
2)Is a finitely generated abelian group?