类似Sylow定理

类似Sylow定理 THEOREMS LIKE SYLOW’S 郑延履 Zheng Yanlü first-author 本文从两方面考虑类似Sylow定理:（一） G的π-Hall子群具备什么条件时,G有π-Sylow性质?得到的定理1统一了Wielandt定理和pycokoв定理。（二） 减弱对π-Hall子群H的要求,问满足什么条件的π-子群必共轭包含在H中?得到的定理2推广了pycokoв定理。 In this paper we show the following theorems. Theorem 1 If H is an π-Hall subgroup of group G and H satisfies follo-wing conditions: 1) H=MN, where M is a nilpotent π 1 -Hall subgroup of H, N is a normal π 2 -Hall subgroup of H and all Sylow subgroups of N are cyclic, π=π 1 ∪π 2 ; 2) M is a trivial intersection set in H （i e for all h∈H, M∩Mn=1 or M）. Then for any π-subgroup K of G, exist g∈G such that KH 0 . Theorem 2 If H is π-Hall subgroup of G such that H is y-group, K which has Sylow tower is an π-subgroup of G, then exist g∈G such that K H 0 . Theorem 1 is unification of Wielandt theorem and Pocoкoв theorem. Th-eorem 2 extends Pycoкoв theorem 类似Sylow定理 极小反例 内y-群 -y group theorem like Sylow’s minimal counterexample minimal non 1988-03-01 2021-04-01 3