The stable subgroup graph

Behnaz Tolue

Abstract


In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1)\cap H_2\neq 1$ or $St_{G}(H_2)\cap H_1\neq 1$. Its planarity is discussed whenever $G$ is an abelian group, $p$-group, nilpotent, supersoluble or soluble group. Finally, the induced subgraph of stable subgroup graph with vertex set whole non-normal subgroups is considered and its planarity is verified for some certain groups.

Keywords


Stabilizer; finite group; planar graph

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DOI: http://dx.doi.org/10.5269/bspm.v36i3.31678



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ISSN 0037-8712 (print) and ISSN 2175-1188 (on-line)

 

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