Groups whose common divisor graph on p-regular clases has diameter three,
Groups whose common divisor graph on p-regular clases has diameter three,
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Date
2024-12-23
Authors
Marc-Kelly Jean Philippe
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Abstract
Let G be a finite p-separable group, for some fixed prime p. Let \Gamma _p(G) be the common divisor graph built on the set of non-central conjugacy classes of p-regular elements of G: this is the graph whose vertices are the conjugacy classes of those non-central elements of G such that p does not divide their orders, and two distinct vertices are adjacent if and only if the greatest common divisor of their lengths is strictly greater than one. The aim of this paper is twofold: to positively answer an open question concerning the maximum possible distance in \Gamma _p(G) between a vertex with maximal cardinality and any other vertex, and to study the p-structure of G when \Gamma _p(G) has diameter three.
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Publicado por la revista: "Mediterranean Journal of Mathematics, 22, 17, 2025;"
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Citation
ean Philippe, M.-K. (2023). Groups whose common divisor graph on p-regular clases has diameter three. Mediterranean Journal of Mathematics, 22, 17.