论文标题
正常的$ 2 $覆盖有限的简单组及其概括
Normal $2$-coverings of the finite simple groups and their generalizations
论文作者
论文摘要
给定有限的$ g $，我们说$ g $的普通覆盖量$γ_w（g）$如果$γ_w（g）$是最小的整数，$ g $承认适当的子群体$ h_1，\ ldots，h_ {γ_w（g）} $ g $ g $ i i i y y y y y y y y y y y y y y y i s y i s in j $ h_i， \ {1，\ ldots，γ_W（g）\} $，通过$ g $的自动形态组中的元素。 我们证明，每个非亚洲简单群体的较弱的覆盖范围至少为$ 2 $，并且我们对获得$ 2 $的非亚伯利亚简单组进行了分类。作为一个应用程序，我们对具有正常覆盖数$ 2 $的非亚洲简单组进行了分类。我们还表明，几乎简单组的弱覆盖量较弱，至少有两个例外。 我们确定弱的覆盖率较弱以及几乎简单的组的正常覆盖量，该组具有零星的简单组。使用类似的方法，我们找到了具有零星简单组的几乎简单组的集团数量。
Given a finite group $G$, we say that $G$ has weak normal covering number $γ_w(G)$ if $γ_w(G)$ is the smallest integer with $G$ admitting proper subgroups $H_1,\ldots,H_{γ_w(G)}$ such that each element of $G$ has a conjugate in $H_i$, for some $i\in \{1,\ldots,γ_w(G)\}$, via an element in the automorphism group of $G$. We prove that the weak normal covering number of every non-abelian simple group is at least $2$ and we classify the non-abelian simple groups attaining $2$. As an application, we classify the non-abelian simple groups having normal covering number $2$. We also show that the weak normal covering number of an almost simple group is at least two up to one exception. We determine the weak normal covering number and the normal covering number of the almost simple groups having socle a sporadic simple group. Using similar methods we find the clique number of the invariably generating graph of the almost simple groups having socle a sporadic simple group.
