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arXiv · 2502.09519

Excluded power graphs of groups

Brian Curtin
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Abstract

Let $\mathcal{X}$ be a set of integers greater than one. The $\mathcal{X}$-excluded power graph of a group $G$ has vertex set $G$ and an edge from $g$ to each power of $g$ other than itself provided that the power is not divisible by any element of $\mathcal{X}$. When $G=H\times K$ for groups $H$ 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 $K$. Partial results for the semidirect product under the same conditions are given. We describe groups whose $\mathcal{X}$-excluded power graphs consist of disjoint directed cliques.

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Brian Curtin. 2025-02-13. Excluded power graphs of groups. https://arxiv.org/abs/2502.09519

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