|
|
Pure Mathematics 2025
块图为线条的有限群
|
Abstract:
在有限群表示论中，有限群的块图具有重要意义。为此，本文证明了块图为线条的有限群可解。
In the representation theory of finite groups, block graphs of finite groups are of significance. As a result, this paper proves that finite groups whose block graphs are a line are solvable.
| [1] | Navarro, G. and Willems, W. (1997) When Is a p-Block a q-Block? Proceedings of the American Mathematical Society, 125, 1589-1591. https://doi.org/10.1090/s0002-9939-97-04135-x |
| [2] | Bessenrodt, C., Malle, G. and Olsson, J.B. (2006) Separating Characters by Blocks. Journal of the London Mathematical Society, 73, 493-505. https://doi.org/10.1112/s0024610705022556 |
| [3] | Navarro, G., Turull, A. and Wolf, T.R. (2005) Block Separation in Solvable Groups. Archiv der Mathematik, 85, 293-296. https://doi.org/10.1007/s00013-005-1407-x |
| [4] | Bessenrodt, C. and Zhang, J. (2008) Block Separations and Inclusions. Advances in Mathematics, 218, 485-495. https://doi.org/10.1016/j.aim.2007.12.010 |
| [5] | Bessenrodt, C. and Zhang, J. (2011) Character Separation and Principal Covering. Journal of Algebra, 327, 170-185. https://doi.org/10.1016/j.jalgebra.2010.10.034 |
| [6] | Brough, J., Liu, Y. and Paolini, A. (2021) The Block Graph of a Finite Group. Israel Journal of Mathematics, 244, 293-317. https://doi.org/10.1007/s11856-021-2192-3 |
| [7] | Isaacs, I.M. (1994) Character Theory of Finite Groups. Academic Press. |
| [8] | Nagao, H. and Tsushima, Y. (1989) Representations of Finite Groups. Academic Press. |
| [9] | Navarro, G. (1998) Characters and Blocks of Finite Groups, London Mathematical Society. Lecture Note Series, Vol. 250. Cambridge University Press. |
| [10] | Huppert, B. and Lempken, W. (2000) Simple Groups of Order Divisible by at Most Four Primes. IEM. |
| [11] | Gorenstein, D. and Lyons, R. (1983) The Local Structure of Finite Groups of Characteristic 2 Type. Memoirs of the American Mathematical Society, 42, Article No. 276. https://doi.org/10.1090/memo/0276 |
