关于有限群分解的一个观察
An observation on factorizations of finite groups
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中文总结 AI 辅助
针对有限群$G$的阶分解$|G|=a_1a_2$，研究人员给出了存在满足条件的子集$A_1,A_2$使得$G=A_1A_2$的充分条件，即$a_1$可由子群链指数的某子族乘积得到。
中文摘要 AI 辅助
给定有限群$G$及其阶的一个分解$|G|=a_1a_2$，我们证明：存在子集$A_1,A_2\subseteq G$满足$|A_1|=a_1$、$|A_2|=a_2$且$G=A_1A_2$的一个充分条件是，存在子群链$\{e\}=G_0<\dots<G_n=G$，使得$a_1$是指数$|G_i:G_{i-1}|$中某个子族的乘积（因此$a_2$是互补子族的乘积）。
英文摘要
Given a finite group $G$ and a factorization of its order, $|G|= a_1 a_2,$ we show that a sufficient condition for there to exist subsets $A_1,\,A_2\subseteq G$ such that $|A_1| = a_1,$ $|A_2| = a_2,$ and $G = A_1\,A_2,$ is that there exist a chain of subgroups $\{e\} = G_0 < \dots < G_n = G$ such that $a_1$ is the product of some subfamily of the indices $|G_i:G_{i-1}|$ (and hence $a_2$ is the product of the complementary subfamily).
发表机构
- University of California Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。
