论文标题
关于嵌入$ \ mathfrak {x} $ - 子群的定理
On embedding theorems for $\mathfrak{X}$-subgroups
论文作者
论文摘要
令$ \ mathfrak {x} $为在子组，同构图像和扩展程序下关闭的有限组。我们研究了一个问题，该问题可以追溯到1963 - 64年的H. Wielandt的讲座：对于给定的$ \ Mathfrak {x} $ - 子组$ k $和Maximal $ \ Mathfrak {x} $ - 子组$ h $，是可以看到$ k $ in Conjugacy的$ k $的嵌入到conjugacy conjugacy actions actions a a a a a a in Projictions的嵌入性。一方面，我们构建了示例，其中$ k $具有与$ h $的某些子组相同的预测，但与$ h $的任何子组都不是共轭的。另一方面，我们证明，如果$ k $正常于子组$ h $的预测，那么$ k $即使在更普遍的情况下，当$ h $是$ h $是一个次级$ \ mathfrak {x} $ - $ subgroup时，$ k $也与$ h $的子组有偶像。
Let $\mathfrak{X}$ be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1963-64: For a given $\mathfrak{X}$-subgroup $K$ and maximal $\mathfrak{X}$-subgroup $H$, is it possible to see embeddability of $K$ in $H$ (up to conjugacy) by their projections onto the factors of a fixed subnormal series. On the one hand, we construct examples where $K$ has the same projections as some subgroup of $H$ but is not conjugate to any subgroup of $H$. On the other hand, we prove that if $K$ normalizes the projections of a subgroup $H$, then $K$ is conjugate to a subgroup of $H$ even in the more general case when $H$ is a submaximal $\mathfrak{X}$-subgroup.
