Let $M$ be a differentiable manifold. Let $G$ be a finite group of smooth maps from $M$ to $M$. Assume that the action of $G$ induced on the tangent space of $M$ at $p\in M$ is nontrivial and irreducible.
What is the definition and interpretation of the action of $G$ being nontrivial and irreducible in this context? Could you provide an introductory reference (textbook) where I can learn about these concepts?