The following theorem is stated in Kurzweil and Stellmacher:
Suppose that the action of a group $A$ on an Abelian group $V$ is coprime and $A$ acts trivially on $\Omega(V)$. Then $A$ acts trivially on $V$.
What is the notation $\Omega(V)$ here? In the text, the authors define $\Omega(G)$ as $$\Omega(G)=\langle x\in G:x^p=1\rangle,$$ where $G$ is a $p$-group. However, I couldn't find this notation for a general group.