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Vol.3 , No. 2, Publication Date: Nov. 5, 2016, Page: 10-14
| [1] | Lijiang Zeng, Research Centre of Zunyi Normal College, Zunyi, China. |
In mathematics, in applied science, even in the natural sciences, group theory has irreplaceable important position. In this article, we introduce derivation process of lower defect groups of group theory through large number of data, at first, some notations about rings, groups, characters of group first, and the using these notations prove some properties of them. Finally we give out the definitions of lower defect group, and prove two interesting theorems about lower defect groups.
Keywords
Conjugate Class, Lower Defect Group, Primitive Idempotent, Brauer Homomorphism
Reference
| [01] | Prof. Joseph Buckley. Finite groups whose minimal subgroups are normal [J]. Mathematische Zeitschrift. 1970 (1), 50-56. |
| [02] | Olsson, J. B. Lower Defect Groups [J]. Comm. Algebra 8, 261-288. MR81g 2004. |
| [03] | P. Schmid. Subgroups permutable with all Sylow subgroups [J]. Journal of Algebra. 1998 (01), 40-44. |
| [04] | Brauer, R. On the connection between the ordinary and the modular characters of groups of finite order [J]. Ann. Of Math. (2) 42, 926-935. MR3, p 196. |
| [05] | N. Y. Deng, Y. Xiao, F. J. Zhou. Nonmonotonic trust region algorithm [J]. Journal of Optimization Theory and Applications. 1993 (02). 70-76. |
| [06] | Gorenstein, D. Finite Groups [M]. Harper and Row, New York, Evanston, London. MR38 229. |
| [07] | Beylkin G, Coifman R, Rokhlin V. Fast wavelet transforms and numerical algorithms I [J]. Communications in Pure Applied Mathematics. 1991 (02), 42-46. |
| [08] | Yangming Li, Yanming Wang, Huaquan Wei. On p-nilpotency of finite groups with some subgroups π-quasinormally embedded [J]. Acta Mathematica Hungarica. 2005 (02), 40-46. |
| [09] | S. Srinivasan. Two sufficient conditions for supersolvability of finite groups [J]. Israel Journal of Mathematics. 1980 (3), 30-36. |
| [10] | Wanzhexian. Geometry of Hamilton matrices and its application Ⅱ[J]. Algebra Colloquium. 1996 (01), 66-69. |
| [11] | Xiuyun Guo, K. P. Shum. On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups [J]. Archiv der Mathematik. 2003 (6), 64-68. |
| [12] | Osima, M. On the induced characters of a group [J]., Proc. Japan Acad. 28, 243-248. MR14, p 351. |
| [13] | Green, J. A. Vorlesungen über Modulare Darstellungstheorie endlicher Gruppen [J]. Vorlesungen aus dem Mathematicschen Institute Giessen Heft 2. MR50 13235. |
| [14] | Brauer, R. On the Cartan invariants of groups of finite order [J]. Ann. Of Math. (2) 42, 53-61, MR2, p 125. |
| [15] | Charles, W. Curtis and Irving Reiner. Representation Theory of Finite Groups and Associative Algebras [M]. A Wiley-Interscience Publication, New York, 1962, pp 25-90. |
| [16] | Green, J. A. On the indecomposable representations of finite group [J]. Math. Z. 70, 430-445. MR24 A1304. |
