I am reading a document it says
A group realization is a map from elements of G to transformations of a space M that is a group homomorphism, i.e. it preserves the group multiplication law. Thus if $T:G \rightarrow T(M): g \mapsto T(g)$ where $T(g)$ is some transformation on M, then T is a homomorphism if $T(g_1 g_2) = T(g_1)T(g_2)$.
I have got a bad feeling about this definition.
If T(M) is transformations on M then how can $T$ also be a map from $G$ to $T(M)$?