论文标题
将非亚伯有限组分为两个子集
Factoring nonabelian finite groups into two subsets
论文作者
论文摘要
一组$ g $据说被分解为子集$ a_1，a_2，\ ldots，a_s \ subseteq g $，如果每个元素$ g $ in $ g $中的每个元素$ g $都可以独特地表示为$ g = g_1g_1g_2 \ ldots g_s g_s $ g_s $，$ g_i \ in_i $ g_i $，$ g_i \ in a_i $，$ i = 1,2,2，s $。我们考虑以下猜想：对于每个有限组$ g $和每个分解$ n = ab $的订单，有一个分解$ g = ab $，$ | a | = a $和$ | b | = b $。我们表明，对此猜想的最小反例必须是一个非亚伯语简单组，并证明每个有限组的猜想的非亚伯构成因子的订单小于$ 10 \，000 $。
A group $G$ is said to be factorized into subsets $A_1, A_2, \ldots, A_s\subseteq G$ if every element $g$ in $G$ can be uniquely represented as $g=g_1g_2\ldots g_s$, where $g_i\in A_i$, $i=1,2,\ldots,s$. We consider the following conjecture: for every finite group $G$ and every factorization $n=ab$ of its order, there is a factorization $G=AB$ with $|A|=a$ and $|B|=b$. We show that a minimal counterexample to this conjecture must be a nonabelian simple group and prove the conjecture for every finite group the nonabelian composition factors of which have orders less than $10\,000$.
