Prove that the notion of group isomorphism is transitive.
My proof so far:
Suppose G, H, and K are groups.
Let the function f be the isomorphism from G onto H, then
with f is onto and 1-1.
That equation should be .
Now let the function t be the isomorphism from H onto K, then
with t is onto and 1-1.
That equation should be .
My plan is to get a function, say X, such that
That equation should be .
First I tried with X = f(t), but it doesn't really work out, so am I at least doing something right here?