论文标题
在与可集成的群体有关的一些问题上
On some questions related to integrable groups
论文作者
论文摘要
如果$ g $是$ h $的派生子组同构的，则可以集成；也就是说，如果$ h'\ simeq g $，在这种情况下，$ h $是$ g $的积分。如果$ g $是$ u $的子组，我们说如果$ g = h'$对于某些$ h \ leq u $，则$ g $是在$ u $中集成的。在这项工作中，我们着重于[1]中提出的两个问题。我们对可集成的几乎简单有限的$ g $进行了分类，我们表明这与可在$ \ mathrm {aut}（s）$中集成的人相同，其中$ s $是$ g $的socle。然后，我们将有限对称组的所有$ 2 $均匀亚组分类为$ s_n $，它们可在$ s_n $中集成。
A group $G$ is integrable if it is isomorphic to the derived subgroup of a group $H$; that is, if $H'\simeq G$, and in this case $H$ is an integral of $G$. If $G$ is a subgroup of $U$, we say that $G$ is integrable within $U$ if $G=H'$ for some $H\leq U$. In this work we focus on two problems posed in [1]. We classify the almost-simple finite groups $G$ that are integrable, which we show to be equivalent to those integrable within $\mathrm{Aut}(S)$, where $S$ is the socle of $G$. We then classify all $2$-homogeneous subgroups of the finite symmetric group $S_n$ that are integrable within $S_n$.
