The intersection graph of a finite simple group has diameter at most 5
نویسندگان
چکیده
Let $G$ be a non-abelian finite simple group. In addition, let $\Delta_G$ the intersection graph of $G$, whose vertices are proper nontrivial subgroups with distinct joined by an edge if and only they intersect nontrivially. We prove that diameter has tight upper bound 5, thereby resolving question posed Shen (2010). Furthermore, 5 is achieved baby monster group certain unitary groups odd prime dimension.
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2021
ISSN: ['0003-889X', '1420-8938']
DOI: https://doi.org/10.1007/s00013-021-01583-3