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Mathematics > Group Theory

arXiv:1812.09363 (math)
[Submitted on 21 Dec 2018]

Title:On the Structure of Finite Groups Associated to Regular Non-Centralizer Graph

Authors:Tariq A. Alraqad, Hicham Saber
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Abstract:The non-centralizer graph of a finite group $G$ is the simple graph $\Upsilon_G$ whose vertices are the elements of $G$ with two vertices $x$ and $y$ are adjacent if their centralizers are distinct. The induced subgroup of $\Upsilon_G$ associated with the vertex set $G\setminus Z(G)$ is called the induced non-centralizer graph of $G$. The notions of non-centralizer and induced non-centralizer graphs were introduced by Tolue in \cite{to15}. A finite group is called regular (resp. induced regular) if its non-centralizer graph (resp. induced non-centralizer graph) is regular. In this paper we study the structure of regular groups as well as induced regular groups. Among the many obtained results, we prove that if a group $G$ is regular (resp. induced regular) then $G/Z(G)$ as an elementary $2-$group (resp. $p-$group).
Subjects: Group Theory (math.GR)
Cite as: arXiv:1812.09363 [math.GR]
  (or arXiv:1812.09363v1 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.1812.09363

Submission history

From: Tariq Alraqad Dr. [view email]
[v1] Fri, 21 Dec 2018 20:37:29 UTC (9 KB)
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