Shen, Rulin Intersection graphs of subgroups of finite groups. (English) Zbl 1208.20022 Czech. Math. J. 60, No. 4, 945-950 (2010). Summary: We classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by B. Csákány and G. Pollák [Czech. Math. J. 19(94), 241-247 (1969; Zbl 0218.20019)]. Cited in 3 ReviewsCited in 30 Documents MSC: 20D30 Series and lattices of subgroups 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 20D06 Simple groups: alternating groups and groups of Lie type Keywords:intersection graphs of subgroups; finite groups; simple groups of Lie type; sporadic simple groups; disconnected graphs Citations:Zbl 0218.20019 × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link References: [1] M. Aschbacher: On the maximal subgroups of the finite classical groups. Invent. Math. 76 (1984), 469–514. · Zbl 0537.20023 · doi:10.1007/BF01388470 [2] J. Bosák: The graphs of semigroups. Theory Graphs Appl., Proc. Symp. Smolenice 1963. 1964, pp. 119–125. [3] R. Carter: Simple Groups of Lie Type. Wiley, London, 1972. · Zbl 0248.20015 [4] I. Chakrabarty, S. Ghosh, T.K. Mukherjee, M.K. Sen: Intersection graphs of ideals of rings. Electronic Notes in Discrete Mathematics 23 (2005), 23–32. · Zbl 1193.05086 · doi:10.1016/j.endm.2005.06.104 [5] B. Csákéany, G. Pollák: The graph of subgroups of a finite group. Czechoslovak Math. J. 19 (1969), 241–247. [6] A. S. Kondrat’ev: Prime graph components of finite simple groups. Math. USSR Sb. 67 (1989), 235–247. · Zbl 0698.20009 · doi:10.1070/SM1990v067n01ABEH001363 [7] D. J. S. Robinson: A Course in the Theory of Groups. Springer, New York-Heidelberg- Berlin, 1982. · Zbl 0483.20001 [8] J. S. Williams: Prime graph components of finite groups. J. Algebra 69 (1981), 487–513. · Zbl 0471.20013 · doi:10.1016/0021-8693(81)90218-0 [9] B. Zelinka: Intersection graphs of finite abelian groups. Czech. Math. J. 25 (1975), 171–174. · Zbl 0311.05119 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.