On power graphs of finite groups with forbidden induced subgraphs

The power graph P(G)P(G) of a finite group GG is a graph whose vertex set is the group GG and distinct elements x,y∈Gx,y∈G are adjacent if one is a power of the other, that is, xx and yy are adjacent if x∈〈y〉x∈〈y〉 or y∈〈x〉y∈〈x〉. We characterize all finite groups GG whose power graphs are claw-free, K1,4K1,4-free or C4C4-free.