论文标题
关于有限组的因素化的注释
A note on factorizations of finite groups
论文作者
论文摘要
在问题的第19.35 kourovka笔记本上，M。H。H. Hooshmand询问是否有有限的组$ g $和分解$ \ mathrm {card}（g）= n_1 \ ldots n_k $，一个人总是可以找到$ a_1，\ ldots $ a_k $ g $ $ g $ $ \ n_1 $ g = a_1 \ ldots a_k; $等价，使得组乘法$ a_1 \ times \ ldots \ times \ times a_k \ to g $是一项培养。 我们表明，对于$ g $，在4个元素上交替组，$ k = 3 $和$（n_1，n_2，n_3）=（2,3,2）$，答案为负。然后，我们概括了证明中使用的一些工具，并注意一个空旷的问题。
In Question 19.35 of the Kourovka Notebook, M. H. Hooshmand asks whether, given a finite group $G$ and a factorization $\mathrm{card}(G)= n_1\ldots n_k$, one can always find subsets $A_1,\ldots,A_k$ of $G$ with $\mathrm{card}(A_i)=n_i$ such that $G=A_1\ldots A_k;$ equivalently, such that the group multiplication map $A_1\times\ldots\times A_k\to G$ is a bijection. We show that for $G$ the alternating group on 4 elements, $k=3$, and $(n_1,n_2,n_3) = (2,3,2)$, the answer is negative. We then generalize some of the tools used in our proof, and note an open question.
