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＜Z₁(H)＜Z₂(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.

Index Terms—л─nilpotent groups, minimal normal subgroups, л-normal groups, weakly s-normal subgroups.

The authors are with School of Mathematics and Statistics, Cangzhou Normal University, Cangzhou, China (email: yurongge999@163.com.).

Cite: Rongge Yu, Ruixia Jiang, "On π-nilpotency of Finite Groups," International Journal of Applied Physics and Mathematics vol. 6, no. 4, pp. 194-199, 2016.