2025/02/13 by Curtin, Brian
#05C20 #05C25 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2502.09519
Let G be a group, and let X be a set of integers greater than one. We consider the directed X-excluded power graph of G, which takes G as its vertex set and has an edge from g to each power of g other than itself provided the power is not divisible by any element of X. We show that when G=H× K for H and K with coprime orders, excluding the prime factors of |H| yields a power graph with a quotient consisting of multiple copies of a quotient of the power graph (no exclusions) of K. For any prime p, we describe the groups whose directed and undirected \p\-excluded power graphs consist of disjoint (directed) cliques.