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On commuting involution graphs for the small Ree groups. (English) Zbl 1490.05109

Summary: Here we investigate the commuting involution graphs for the small Ree groups, analyzing their disk structure and showing their diameter is either 3 or 4.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C12 Distance in graphs
20E99 Structure and classification of infinite or finite groups
Full Text: DOI

References:

[1] Bates, C.; Bundy, D.; Perkins, S.; Rowley, P., Commuting involution graphs in special linear groups, Commun. Algebra, 32, 11, 4179-4196 (2004) · Zbl 1074.20033 · doi:10.1081/AGB-200034023
[2] Cannon, J. J.; Playoust, C., An Introduction to Algebraic Programming with Magma [draft] (1997), Berlin: Springer-Verlag, Berlin
[3] Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; Wilson, R. A., Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups. With Computational Assistance from J. G. Thackray (1985), Eynsham: Oxford University Press, Eynsham · Zbl 0568.20001
[4] Everett, A., Commuting involution graphs for 3-dimensional unitary groups, Electron. J. Combin, 18, 1, 11 (2011) · Zbl 1217.05083 · doi:10.37236/590
[5] Everett, A.; Rowley, P., Commuting Involution Graphs for 4-dimensional Projective Symplectic Groups, Graphs Combin, 36, 4, 959-1000 (2020) · Zbl 1442.05085 · doi:10.1007/s00373-020-02156-x
[6] Gorenstein, D., Finite Groups (1980), New York: Chelsea Publishing Co, New York · Zbl 0463.20012
[7] Kleidman, P. B., The maximal subgroups of the Chevalley groups \(####\) with q odd, the Ree groups \(####\) and their automorphism groups, J. Algebra, 117, 1, 30-71 (1988) · Zbl 0651.20020
[8] Levchuk, V. M.; Nuzhin, Y. N., The structure of Ree groups (Russian), Algebra i Logika, 24, 1, 26-41 (1985) · Zbl 0581.20025
[9] Ree, R., A family of simple groups associated with the simple Lie algebra of type G_2, Amer. J. Math, 83, 3, 432-462 (1961) · Zbl 0104.24705 · doi:10.2307/2372888
[10] Ward, H., On Ree’s Series of Simple Groups, Trans. Am. Math. Soc, 121, 1, 62-89 (1966) · Zbl 0139.24902
[11] Wilson, R. A., The Finite Simple Groups, volume 251 of Graduate Texts in Mathematics (2009), London: Springer-Verlag, London · Zbl 1203.20012
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