论文标题
超溶剂补充的结合条件和非审理作用的固定点结果
Conjugacy conditions for supersoluble complements of an abelian base and a fixed point result for non-coprime actions
论文作者
论文摘要
我们证明，当且仅当每个Prime $ p $，一个sylow $ p $ -subgroup of一个补充的情况下，在有限的拆分扩展中，阿贝尔基地的两个超溶剂是共轭的。 As a corollary, we find that any two supersoluble complements of an abelian subgroup $N$ in a finite split extension $G$ are conjugate if and only if, for each prime $p$, there exists a Sylow $p$-subgroup $S$ of $G$ such that any two complements of $S\cap N$ in $S$ are conjugate in $G$.特别是，限制超溶小组使我们能够减轻D. G. Higman的规定，即$ S $ S $中的$ S \ CAP n $的补充是在$ s $之内结合的。然后，我们考虑小组动作并获得类似于格劳伯曼引理类似的非摄取行动的固定点结果。
We demonstrate that two supersoluble complements of an abelian base in a finite split extension are conjugate if and only if, for each prime $p$, a Sylow $p$-subgroup of one complement is conjugate to a Sylow $p$-subgroup of the other. As a corollary, we find that any two supersoluble complements of an abelian subgroup $N$ in a finite split extension $G$ are conjugate if and only if, for each prime $p$, there exists a Sylow $p$-subgroup $S$ of $G$ such that any two complements of $S\cap N$ in $S$ are conjugate in $G$. In particular, restricting to supersoluble groups allows us to ease D. G. Higman's stipulation that the complements of $S\cap N$ in $S$ be conjugate within $S$. We then consider group actions and obtain a fixed point result for non-coprime actions analogous to Glauberman's lemma.
