Non-solvable graphs of groups

26 Sep 2019 Bhowal Parthajit Nongsiang Deiborlang Nath Rajat Kanti

Let $G$ be a group and $Sol(G)=\{x \in G : \langle x,y \rangle \text{ is solvable for all } y \in G\}$. We associate a graph $\mathcal{NS}_G$ (called the non-solvable graph of $G$) with $G$ whose vertex set is $G \setminus Sol(G)$ and two distinct vertices are adjacent if they generate a non-solvable subgroup... (read more)

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  • GROUP THEORY