The stable subgroup graph
2018 ◽
Vol 36
(3)
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pp. 129-139
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.
2019 ◽
Vol 12
(05)
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pp. 1950081
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1974 ◽
Vol 17
(3)
◽
pp. 305-318
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2013 ◽
Vol 05
(03)
◽
pp. 1350012
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2016 ◽
Vol 95
(1)
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pp. 38-47
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Keyword(s):
2013 ◽
Vol 13
(01)
◽
pp. 1350064
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