标题： 仿射群中小维数的正常2覆盖 显示英文标题

标题： Normal 2-coverings in affine groups of small dimension

摘要： 一个有限群$G$有一个正规$2$-覆盖，如果存在两个真子群$H$和$K$满足$G=\bigcup_{g\in G}H^g\cup\bigcup_{g\in G}K^g$。 为了递归地确定接受正规$2$-覆盖的有限群，确定所有接受正规$2$-覆盖的有限群$G$是重要的，其中$G$的任何真商群都不接受这样的覆盖。 使用来自 O'Nan-Scott 定理的术语，Garonzi 和 Lucchini 已经证明这些群分为四类：乘积作用、几乎单、仿射和对角线。 在本文中，我们开始对仿射情况进行初步研究。 显示英文摘要

摘要： A finite group $G$ admits a normal $2$-covering if there exist two proper subgroups $H$ and $K$ with $G=\bigcup_{g\in G}H^g\cup\bigcup_{g\in G}K^g$. For determining inductively the finite groups admitting a normal $2$-covering, it is important to determine all finite groups $G$ possessing a normal $2$-covering, where no proper quotient of $G$ admits such a covering. Using terminology arising from the O'Nan-Scott theorem, Garonzi and Lucchini have shown that these groups fall into four natural classes: product action, almost simple, affine and diagonal. In this paper, we start a preliminary investigation of the affine case.