共轭类长两两最大公因子至多有两个素因子的有限单群
Finite Simple Groups in Which Any Two Different Conjugacy Class Lengths Have at Most Two Prime Divisors in Common
DOI: 10.12677/PM.2021.1112222, PDF, HTML,    科研立项经费支持
作者: 张耀芳：九江职业大学师范学院，江西 九江；刘燕俊：江西师范大学数学与统计学院，江西 南昌
关键词: 有限单群；共轭类；最大公因子；素因子；Finite Simple Group； Conjugacy Class； Greatest Common Divisor； Prime Divisor
摘要: 本文证明了A5是唯一满足任意两个不同共轭类长的最大公因子至多有两个(不一定不同)素因子的有限单群。
Abstract: This paper shows that A5 is the only finite simple group such that the greatest common divisor of any pair of its different conjugacy class lengths has at most two (not necessarily different) prime divisors.
文章引用：张耀芳, 刘燕俊. 共轭类长两两最大公因子至多有两个素因子的有限单群[J]. 理论数学, 2021, 11(12): 1993-2002. https://doi.org/10.12677/PM.2021.1112222

参考文献

[1] Khukhro, E.I. and Mazurov, V.D. (2021) Unsolved Problems in Group Theory: The Kourovka Notebook. arXiv:1401.0300 [math.GR]
[2] Lewis, M. (2005) The Number of Irreducible Character Degrees of Solvable Groups Satisfying the One-Prime Hypothesis. Algebras and Representation Theory, 8, 479-497.
https://doi.org/10.1007/s10468-005-3596-1
[3] Hamblin, J. and Lewis, M. (2012) Solvable Groups Satisfying the Two-Prime Hypothesis, II. Algebras and Representation Theory, 15, 1099-1130.
https://doi.org/10.1007/s10468-011-9281-7
[4] Liu, Y., Song, X. and Zhang, J. (2015) Nonsolvable Groups Satisfying the Prime-Power Hypothesis. Journal of Algebra, 442, 455-483.
https://doi.org/10.1016/j.jalgebra.2014.02.010
[5] Du, N. and Lewis, M.L. (2017) The Prime-Power Hypothesis and Solvable Groups. Archiv der Mathematik (Basel), 109, 301-303.
https://doi.org/10.1007/s00013-017-1085-5
[6] Camina, A.R. and Camina, R.D. (2017) One-Prime Power Hypothesis for Conjugacy Class Sizes. International Journal of Group Theory, 6, 13-19.
[7] Dornhoff, L. (1971) Group Representation Theory, Part A: Ordinary Representation Theory. Marcel Dekker, New York.
[8] Gorenstein, D. (1982) Finite Simple Groups. An Introduction to Their Classification. University Series in Mathematics. Plenum Publishing Corp., New York.
https://doi.org/10.1007/978-1-4684-8497-7 1
[9] The GAP Group (2015) GAP-Groups, Algorithms, and Programming, Version 4.7.9.
http://www.gap-system.org
[10] 徐明昭. 有限群初步[M]. 北京: 科学出版社, 2013.

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