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Communications in Algebra Volume 51, 2023 - Issue 9
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Research Articles

Cubic graphical regular representations of Ree groups

Teng Fanga School of Mathematics, Southeast University, Nanjing, P. R. China
,
Binzhou Xiab School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia
,
Shasha Zhengb School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, AustraliaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-9025-5634
ORCID Icon &
Sanming Zhoub School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia
Pages 3729-3733 | Received 29 Aug 2021, Accepted 01 Mar 2023, Published online: 21 Mar 2023

References

  • Bäärnhielm, H. (2014). Recognising the small Ree groups in their natural representations. J. Algebra 416:139–166. DOI: 10.1016/j.jalgebra.2014.06.017.
  • Chao, C. Y. (1964). On a theorem of Sabidussi. Proc. Amer. Math. Soc. 15:291–292. DOI: 10.1090/S0002-9939-1964-0159321-0.
  • Fang, X. G., Li, C. H., Wang, J., Xu, M. Y. (2002). On cubic Cayley graphs of finite groups. Discrete Math. 244:67–75. DOI: 10.1016/S0012-365X(01)00075-9.
  • Godsil, C. D. (1981). GRRs for nonsolvable groups. Algebraic Methods in Graph Theory (Szeged, 1978). Colloq. Math. Soc. Jannos Bolyai 25:221–239.
  • Godsil, C. D. (1983). The automorphism groups of some cubic Cayley graphs. Eur. J. Combin. 4(1):25–32. DOI: 10.1016/S0195-6698(83)80005-5.
  • Kleidman, P. B. (1988). The maximal subgroups of the Chevalley groups G2(q) with q odd, the Ree groups 2G2(q), and their automorphism groups. J. Algebra 117:30–71. DOI: 10.1016/0021-8693(88)90239-6.
  • Leemans, D., Liebeck, M. W. (2017). Chiral polyhedra and finite simple groups. Bull. London Math. Soc. 49:581–592. DOI: 10.1112/blms.12041.
  • Levchuk, V. M., Nuzhin, Y. N. (1985). Structure of Ree groups. Alg. i Log. 24(1):16–26. DOI: 10.1007/BF01978703.
  • Li, J.J., Xia, B., Zhang, X.Q. and Zheng, S. (2022). Cubic graphical regular representations of PSU3(q). Discrete Math. 345(10): 112982. DOI: 10.1016/j.disc.2022.112982.
  • Moori, J., Rodrigues, B. G., Saeidi, A., Zandi, S. (2019). Some symmetric designs invariant under the small Ree groups. Commun. Algebra 47(5):2131–2148. DOI: 10.1080/00927872.2018.1530245.
  • Moori, J., Rodrigues, B. G., Saeidi, A., Zandi, S. (2020). Designs from maximal subgroups and conjugacy classes of Ree groups. Adv. Math. Commun. 14(4):603–611. DOI: 10.3934/amc.2020033.
  • Nowitz, L. A. (1968). On the non-existence of graphs with transitive generalized dicyclic groups. J. Combin. Theory Ser. A 4(1):49–51. DOI: 10.1016/S0021-9800(68)80086-9.
  • Pierro, E. (2016). The Möbius function of the small Ree groups. Australas. J. Combin. 66(2):142–176.
  • Ree, R. (1961). A family of simple groups associated with the simple Lie algebra of type (G2). Amer. J. Math. 83(8):432–462. DOI: 10.2307/2372888.
  • Sabidussi, G. (1964). Vertex-transitive Graphs. Monatsh. Math. 68:426–438. DOI: 10.1007/BF01304186.
  • Spiga, P. (2018). Cubic graphical regular representations of finite non-abelian simple groups. Commun. Algebra 46(6):2440–2450. DOI: 10.1080/00927872.2017.1383997.
  • Watkins, M. E. (1971). On the action of non-abelian groups on graphs. J. Combin. Theory Ser. B 11(2):95–104. DOI: 10.1016/0095-8956(71)90019-0.
  • Wilson, R. A. (2009). The Finite Simple Groups. Graduate Texts in Mathematics, 251. London: Springer.
  • Xia, B., Fang, T. (2016). Cubic graphical regular representations of PSL2(q). Discrete Math. 339(8):2051–2055. DOI: 10.1016/j.disc.2016.03.008.
  • Xia, B. (2020). Cubic graphical regular representations of PSL3(q). Discrete Math. 343(1):111646. DOI: 10.1016/j.disc.2019.111646.
  • Xia, B. (2020). On cubic graphical regular representations of finite simple groups. J. Combin. Theory Ser. B 141:1–30. DOI: 10.1016/j.jctb.2019.06.002.
  • Xia, B., Zheng, S., Zhou, S. (2022). Cubic graphical regular representations of some classical simple groups. J. Algebra 612:256–280. DOI: 10.1016/j.jalgebra.2022.08.027.
  • Xu, M., Xu, S. (2004). Symmetry properties of Cayley graphs of small valencies on the alternating group A5. Sci. China Ser. A-Math. 47(4):593–604. DOI: 10.1360/03ys0065.

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