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Title
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Orders of Groups Characterised by Their Power Graphs
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Type
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Presentation
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Keywords
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power graph, conformal groups.
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Abstract
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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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Researchers
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Mahsa Mirzargar (First Researcher)
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