Let's $f:G\to R$, where G is topological group. We denote by Mg group of all real valued functions on G.Fix $a \in G$. We define $f_a(x):=f(ax)$ for all $x \in G$
Now define $h_a(f):=f_a$ we know that $h_a:Mg \to Mg$. Define $\varphi(a):=h_a$ We know, that this is isometry, then denote group of all isometries of space Mg into itself by Is(Mg). I should show that $\varphi$ is a homomorphism of groups Mg and Is(Mg). But probably throught great number of signs i have had only bad ideas. Please help.