Abstract
We prove that each projective special unitary group G can be characterized using only the set of element orders of G and the order of G.
Similar content being viewed by others
References
Shi Wujie, A new characterization of the sporadic simple groups in group theory, in Proceedings of the 1987 Singapore Group Theory Conference, Berlin-New York: Walter de Gruyter, 1989, 531–540.
Mazurov, V. D., Khukhro, E. I., Unsolvable Problems in Group Theory—The Kourovka Notebook, Novosibirsk: Russian Academy of Science, 1999, 87.
Shi Wujie, A new characterization of some simple groups of Lie type, Contemporary Math., 1989, 82: 171–180.
Shi Wujie, The pure quantitative characterization of finite simple groups (I), Progress in Natural Science, 1994, 4(3): 316–326.
Shi Wujie, Bi Jianxing, A characteristic property for each finite projective special linear group, Lecture Notes in Math., 1990, 1456: 171–180.
Shi Wujie, Bi Jianxing, A characterization of Suzuki-Ree groups, Science in China, Series A, 1991, 34(1): 14–19.
Shi Wujie, Bi Jianxing, A new characterization of the alternating groups, Southeast Asian Bull. Math., 1992, 16(1): 81–90.
An Jianbei, Shi Wujie, The characterization of finite simple groups with no elements of order six by their element orders, Comm. in Algebra, 2000, 28(7): 3351–3358.
Shi Wujie, A characterization of U 3(2n) by their element orders, J. Southwest China Normal University (Natural Science), 2000, 25(4): 353–360.
Mazurov, V. D., Xu Mingchun, Cao Hongping, Recognition of finite simple groups L3(2m) and U3(2m) by their element orders, Algebra and Logic, 2000, 39(5): 324–334.
Shi Wujie, On simple K3-groups, J. Southwest China Normal University (Natural Science) (in Chinese), 1988, 13(3): 1–4.
Mazurov, V. D., Recognition of finite groups by a set of orders of their elements, Algebra and Logic, 1998, 37(6): 371–379.
Williams, J. S., Prime graph components of finite groups, J. Algebra, 1981, 69(2): 487–513.
Higman, G., Finite groups in which every element has prime power order, J. London Math. Soc., 1957, 32: 335–342.
Passman, D. S., Permutation Groups, New York: W. A. Benjamin, 1968.
Shi Wujie, Yang Wenze, The finite groups all of whose elements are of prime power order, J. Yunnan Educational College (in Chinese), 1986, 1(1): 2–10.
Conway, J. H., Curtis, R. T., Parker, S. P. et al., An ATLAS of Finite Groups, Oxford: Clarendon Press, 1985.
Feit, W., Seitz, G. M., On finite rational groups and related topics, Illinois J. Math., 1989, 33(1): 103–131.
Zsigmondy, K., Zur theorie der Potenzreste, Monatsh. Math. Phys., 1892, 3: 265–284.
Curtis, C. W., Kantor, W. M., Seitz, G. M., The 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc., 1976, 218: 1–59.
Iiyora, N., Yamaki, H., Prime graph components of the simple groups of Lie type over the field of even characteristic, J. Algebra, 1993, 155: 335–343.
Shi Wujie, A characterization of the finite simple group U 4(3), Analele Universită ţii din Timi,soara, Ser. Ştiinţe Mat., 1992, 30(2): 319–323.
Shi Wujie, Li Huiling, A characteristic property of M 12 and PSU(6, 2), Acta Math. Sinica (in Chinese), 1989, 32(6): 758–764.
Weir, A. J., Sylow p-subgroups of the general linear group over finite fields of characteristic p, Proc. Amer. Math. Soc., 1955, 6: 454–464.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cao, H., Shi, W. Pure quantitative characterization of finite projective special unitary groups. Sci. China Ser. A-Math. 45, 761–772 (2002). https://doi.org/10.1360/02ys9083
Received:
Issue Date:
DOI: https://doi.org/10.1360/02ys9083