Isomorphism of A, B ∩ C: Techniques

[tgt]

What would be the technique to show A is isomorphic to (B intersection C)?where A, B and C are groups.

 

[HallsofIvy]

The obvious way: construct an iosomorphism from A to (B intersection C).

Of course, how you construct such an isomorphism will depend on exactly what A, B, and C are, since whether they are isomorphic depends on what they are!

That is, find a function that assigns, to every member of A, a specific member of B intersect C and then show that it:
1) preserves the operation: f(x*y)= f(x)*f(y)
2) maps the indentity in A to the identity in B.
3) is one-to-one.
4) maps A "onto" B intersect C.