关于奇阶群的不变量E（G）
On the invariant E(G) for groups of odd order
摘要：
设$G$是一个乘法写的有限群.我们用$\mathsf E(G)$表示最小整数$t$，使得$G$中的每个$t$元素序列包含长度为$|G|$的乘积1子序列。1961年，Erdens-Ginzburg和Ziv证明了对每个有限可解群$G$有$\mathsf E(G)\leq 2|G|-1$，这个结果被称为Erdens-Ginzburg-Ziv定理。2010年，Gao和Li将这个结果改进为$\mathsf E(G)\leq\frac{7|G|}{4}-1$，并证明了$\mathsf E(G)\leq \frac{3|G|}{2}$对任意有限非循环群成立.本文对所有奇数阶有限非循环群证实了猜想。
英文摘要：
Let $G$ be a multiplicatively written finite group. We denote by $\mathsf E(G)$ the smallest integer $t$ such that every sequence of $t$ elements in $G$ contains a product-one subsequence of length $|G|$. In 1961, Erdős, Ginzburg and Ziv proved that $\mathsf E(G)\leq 2|G|-1$ for every finite solvable group $G$ and this result is well known as the Erdős-Ginzburg-Ziv Theorem. In 2010, Gao and Li improved this result to $\mathsf E(G)\leq\frac{7|G|}{4}-1$ and they conjectured that $\mathsf E(G)\leq \frac{3|G|}{2}$ holds for any finite non-cyclic group. In this paper, we confirm the conjecture for all finite non-cyclic groups of odd order.
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