Arithmetical conditions on element orders and group structure
HTML articles powered by AMS MathViewer
- by Ji Ping Zhang PDF
- Proc. Amer. Math. Soc. 123 (1995), 39-44 Request permission
Abstract:
General results are provided on bounding the number of different prime factors of the order of finite groups in terms of the number for the order of elements.References
- Rolf Brandl, Finite groups all of whose elements are of prime power order, Boll. Un. Mat. Ital. A (5) 18 (1981), no. 3, 491–493 (English, with Italian summary). MR 633687
- Michel Broué and Gunter Malle, Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis, Math. Ann. 292 (1992), no. 2, 241–262 (French). MR 1149033, DOI 10.1007/BF01444619
- Roger W. Carter, Finite groups of Lie type, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1985. Conjugacy classes and complex characters; A Wiley-Interscience Publication. MR 794307
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, $\Bbb {ATLAS}$ of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups; With computational assistance from J. G. Thackray. MR 827219
- Pamela A. Ferguson, Lengths of conjugacy classes of finite solvable groups. II, J. Algebra 154 (1993), no. 1, 223–227. MR 1201921, DOI 10.1006/jabr.1993.1013
- David Gluck, Primes dividing character degrees and character orbit sizes, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 45–46. MR 933396
- P. Hall and Graham Higman, On the $p$-length of $p$-soluble groups and reduction theorems for Burnside’s problem, Proc. London Math. Soc. (3) 6 (1956), 1–42. MR 72872, DOI 10.1112/plms/s3-6.1.1
- Graham Higman, Finite groups in which every element has prime power order, J. London Math. Soc. 32 (1957), 335–342. MR 89205, DOI 10.1112/jlms/s1-32.3.335
- Bertram Huppert, Inequalities for character degrees of solvable groups, Arch. Math. (Basel) 46 (1986), no. 5, 387–392. MR 847081, DOI 10.1007/BF01210777
- Hua Lo-keng, Su lung tao yeng, Science Press, Peking, 1964 (Chinese). MR 0194380
- Olaf Manz, Arithmetical conditions on character degrees and group structure, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 65–69. MR 933400 W. J. Shi, Characterization of finite simple groups and related topics, Adv. in Math. (China) 20 (1991), 135-141.
- Michio Suzuki, Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc. 99 (1961), 425–470. MR 131459, DOI 10.1090/S0002-9947-1961-0131459-5
- J. S. Williams, Prime graph components of finite groups, J. Algebra 69 (1981), no. 2, 487–513. MR 617092, DOI 10.1016/0021-8693(81)90218-0
- Ji Ping Zhang, Finite groups with many conjugate elements, J. Algebra 170 (1994), no. 2, 608–624. MR 1302859, DOI 10.1006/jabr.1994.1356
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 39-44
- MSC: Primary 20D60
- DOI: https://doi.org/10.1090/S0002-9939-1995-1239809-1
- MathSciNet review: 1239809