# Thread:

1. ## isomorphisms

How does one show that a G is isomorphic to the external direct product of H and K if G=HK and if H and K have unique elements.
Also how does one apply this to proving U(15) is isomorphic to the external direct product of U(3) and U(5) and how would you show if U(15) is cyclic or not?

2. Originally Posted by morganfor
How does one show that a G is isomorphic to the external direct product of H and K if G=HK and if H and K have unique elements.
Also how does one apply this to proving U(15) is isomorphic to the external direct product of U(3) and U(5) and how would you show if U(15) is cyclic or not?
Are you asking to prove if $H,K \triangleleft G$ with $G = HK$ and $H\cap K = \{ e \}$ then $G\simeq H\times K$?

3. yes but H and K are not normal to G
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