doi: 10.17706/ijapm.2016.6.4.194-199
On π-nilpotency of Finite Groups
Rongge Yu
,
- School of Mathematics and Statistics, Cangzhou Normal University, Cangzhou, China
Abstract
A group G is called л-nilpotent, л a set of primes, if G has a normal л’-subgroup N with G/N a nilpotent л-group. Let H be a nilpotent л-Hall subgroup of G, 1＜Z<sub>1</sub>(H)＜Z<sub>2</sub>(H) ＜┄＜Zn(H)=H be the upper central series of H. If every Zi(H) is weakly closed in H (about G). Then we say that the upper central series of H is weakly closed in H (about G). Let H be a subgroup of a finite group G. We call H weakly s-normal in G if there exists a Sylow p-subgroup Sp which is permutable with H for every prime p∣|G|. In this paper, with the conception above, several determine theorems for G to be a л─nilpotent group are given and some properties about л─nilpotent groups are considered. Several results about nilpotent groups are generalized.
Keywords
- л─nilpotent groups
- minimal normal subgroups
- л-normal groups
- weakly s-normal subgroups
How to Cite
Rongge Yu and Ruixia Jiang, "On π-nilpotency of Finite Groups," International Journal of Applied Physics and Mathematics, vol. 6, no. 4, pp. 194-199, 2016. https://doi.org/ 10.17706/ijapm.2016.6.4.194-199
Copyright & License
Copyright © 2016 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).