Akbari, B.; Lewis, Mark L.; Mirzajani, J.; Moghaddamfar, A. R. The solubility graph associated with a finite group. (English) Zbl 07276751 Int. J. Algebra Comput. 30, No. 8, 1555-1564 (2020). MSC: 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks 20D05 Finite simple groups and their classification 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:finite group; soluble group; solubility graph PDF BibTeX XML Cite \textit{B. Akbari} et al., Int. J. Algebra Comput. 30, No. 8, 1555--1564 (2020; Zbl 07276751) Full Text: DOI References: [1] Abe, S. and Iiyori, N., A generalization of prime graphs of finite groups, Hokkaido Math. J.29(2) (2000) 391-407. · Zbl 0965.20008 [2] P. Bhowal, D. Nongsiang and R. K. Nath, A note on solvable graphs of finite groups, preprint (2019), arXiv:1903.01755v1 [Math.GR]. [3] Bondy, J. A. and Murty, U. S. R., Graph Theory (Springer, New York, 2008). · Zbl 1134.05001 [4] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of Finite Groups (Clarendon Press, Oxford University Press, Eynsham, 1985). · Zbl 0568.20001 [5] Delizia, C., Moravec, P. and Nicotera, C., Finite groups in which some property of two-generator subgroups is transitive, Bull. Austral. Math. Soc.75(2) (2007) 313-320. · Zbl 1119.20020 [6] Dickson, L. E., Linear Groups: With an Exposition of the Galois Field Theory (Dover Publications Inc., New York, 1958). · Zbl 0082.24901 [7] Guralnick, R., Kunyavskiĭ, B., Plotkin, E. and Shalev, A., Thompson-like characterization of the solvable radical, J. Algebra300(1) (2006) 363-375. · Zbl 1118.20021 [8] Hagie, M., The diameter of the solvable graph of a finite group, Hokkaido Math. J.29(3) (2000) 553-561. · Zbl 0969.20011 [9] Huppert, B., Endliche Gruppen, I. (Springer-Verlag, Berlin-New York, 1967). [10] Huppert, B. and Blackburn, N., Finite Groups III (Springer-Verlag, Berlin, 1982). · Zbl 0514.20002 [11] Isaacs, I. M., Finite Group Theory, , Vol. 92 (American Mathematical Society, Providence, 2008). · Zbl 1169.20001 [12] D. Hai-Reuven, Nonsolvable graph of a finite group and solvabilizers, preprint (2013), arXiv:1307.2924v1 [math. GR]. [13] Suzuki, M., On a finite group with a partition, Arch. Math. (Basel)12 (1961) 241-254. · Zbl 0107.25902 [14] Suzuki, M., On a class of doubly transitive groups, Ann. Math. (2)75 (1962) 105-145. · Zbl 0106.24702 [15] Thompson, J. G., Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc.74 (1968) 383-437. · Zbl 0159.30804 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.