论文标题
具有相同功率图的有限组
Finite groups with the same Power graph
论文作者
论文摘要
G组G的功率图P（G）是一个带顶点集G的图形，当一个顶点U和V相邻时，并且仅当一个是另一个的幂时。在本文中，我们提出和研究以下问题：对于哪些自然数n，每两组n级n具有同构功率图是同构的？特别是，我们确定所有这些n均无立方体，不是16的多倍。
The power graph P(G) of a group G is a graph with vertex set G, where two vertices u and v are adjacent if and only if one is the 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, we determine prove that all such n are cube-free and are not multiples of 16. Moreover, we show that if two finite groups have isomorphic power graphs and one of them is nilpotent or has a normal Hall subgroup, the same is true with the other one.
