On power graphs of finite groups with forbidden induced subgraphs

The power graph $\mathcal{P}(G)$ of a finite group $G$ is a graph whose vertex set is the group $G$ and distinct elements $x,y\in G$ are adjacent if one is a power of the other, that is, $x$ and $y$ are adjacent if $x\in\langle y\rangle$or$y\in\langle x\rangle$\mathrm{.}Wecharacterizeallfinitegroups$G$whosepowergraphsareclaw-free,$K_{1,4}$-freeor$C_4$-free.