2020/10/28 by Mahsa Mirzargar, Mirzargar, M., Raffaele Scapellato +1 · 1 citation
Computer Science · Engineering · Mathematics · #05C69 #Advanced Graph Theory Research #F.2.2 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2010.15038
openalex publication_date 2020/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.