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Characterization by intersection graph of some families of finite nonsimple groups

Hossein Shahsavari, Behrooz Khosravi (2021)

Czechoslovak Mathematical Journal

For a finite group G , Γ ( G ) , the intersection graph of G , is a simple graph whose vertices are all nontrivial proper subgroups of G and two distinct vertices H and K are adjacent when H K 1 . In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.

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