Thread: Group Homomorphism Mapping

1. Group Homomorphism Mapping

Hi all, need to get this done by tonight. Any help would be muh appreciated

2. Hi, has this got anything to do with proving the inverse, identity and closure axioms? If so, can someone start me off please?

3. Originally Posted by moolimanj
Hi, has this got anything to do with proving the inverse, identity and closure axioms? If so, can someone start me off please?
Show what you did. Show how you applied the definitions of homomorphism here.

4. Can you start me off please - i really dont know where to begin

5. Your mapping does not make so much sense. What do $\displaystyle \phi: G\times G\mapsto H$ mean? It can only make sense if $\displaystyle H = G\times G$. Because $\displaystyle \phi(g_1,g_2) = (g_1,g_1)$ and this needs to be an element of $\displaystyle H$, for that to happen we need $\displaystyle H=G\times G$. Thus, I will assume that.

The first step is to show this is a group homomorphism. $\displaystyle \phi ((g_1,g_2)(g_1',g_2')) = \phi(g_1g_1',g_2g_2') = (g_1g_1',g_2g_2') = (g_1,g_2)(g_1',g_2') = \phi(g_1,g_2)\phi(g_1',g_2')$.