|
|
- 2015
关于有限亚循环2-群全形的整群环的一个注记
|
Abstract:
摘要： 设G是有限亚循环2-群,记/HolG为G的全形。证明了在整群环ZHolG中下面等式成立:NU(ZHolG)(G)=G·Z(ZHolG)。
Abstract: Let G be a finite metacyclic 2-group and let HolG be its holomorph. It is proved that the equality NU(ZHolG)(G)=G·Z(ZHolG) holds in the integral group ring ZHolG
| [1] | LI Zhengxing, HAI Jinke. The normalizer property for integral group rings of finite solvable <em>T</em>-groups[J]. J Group Theory, 2012, 15(2):237-243. |
| [2] | LI Zhengxing, HAI Jinke. Coleman automorphisms of holomorphs of finite abelian groups[J]. Acta Mathematica Sinica, 2014, 30(9):1549-1554. |
| [3] | LI Zhengxing, HAI Jinke. Coleman automorphisms of standard wreath products of nilpotent groups by groups with prescribed Sylow 2-subgroups [J]. Journal of Algebra and its Applications, 2014, 13(5):1350156.1-1350156.9. |
| [4] | MAZUROV D. Finite groups with metacyclic Sylow 2-subgroups [J]. Sibirskii Matematicheskii Zhurnal, 1967, 8:966-982. |
| [5] | COLEMAN D B. On the modular group ring of a <em>p</em>-group [J]. Proc Amer Math Soc, 1964, 15:511-514. |
| [6] | HERTWECK M. Class-preserving automorphisms of finite groups [J]. J Algebra, 2001, 241 (1):1-26. |
| [7] | HERTWECK M, JESPERS E. Class-preserving automorphisms and the normalizer property for Blackburn groups [J]. J Group Theory, 2009, 12(1):157-169. |
| [8] | LI Yuanlin. The normalizer property of a metabelian group in its integral group ring [J]. J Algebra, 2002, 256(2):343-351. |
| [9] | LI Yuanlin, SEHGAL S K, PARMENTER M M. On the nomalizer property for integral group rings[J]. Comm Algebra, 1999, 27(9):4217-4223. |
| [10] | SEHGAL S K. Units in integral group rings [M]. New York: Longman Scientific ＆ Technical, 1996. |
| [11] | KURZWEIL H, STELLMACHER B. The theory of finite groups: an introduction [M]. New York: Springer-Verlag, 2003. |
