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چکیده
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The power graph $P(G)$ of a group $G$ is the graph whose vertex set is the group elements and two elements are adjacent if one is a power of the other. In this paper, we raise and study the following question: For which natural numbers $n$ every two groups of order $n$ with isomorphic power graphs are isomorphic? In particular, it is proved that all such odd number $n$ are cube-free and also they are not multiples of $16$ in general.
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