Proof:
G is an infinite cyclic group, then G=<a>, where a is a generator of G. Now we can define a map f from G to Z as follows:
for any b in G, b=a^i ...
Solution Summary
This is a proof regarding isomorphisms and infinite cyclic groups.
Isomorphism proof. Show that a homomorphism from a field onto a ring with more than one element must be an isomorphism. ... Therefore, g is an isomorphism. ...
... vertices and the same number of edges, and that the degree of a vertex of a graph is equal to the degree of the image of that vertex under a graph isomorphism. ...
... extension obtained by adjoining a root of g. Determine the number of isomorphisms from K to L. (It is not necessary to explicitly describe such an isomorphism). ...
