A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two \({\mathbb {Z}}/2\)- spaces is equal to the minimum of their \({\mathbb {Z}}/2\)-indexes. The main purpose of this article is to study the topological version of the Hedetniemi conjecture for G-spaces. Indeed, we show that the topological Hedetniemi conjecture cannot be valid for general pairs of G-spaces. More precisely, we show that this conjecture can possibly survive if the group G is either a cyclic p-group or a generalized quaternion group whose size is a power of 2.

中文翻译：

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Hedetniemi 等变空间猜想的拓扑版本

著名的 Hedetniemi 猜想的拓扑版本说：两个\({\mathbb {Z}}/2\) - 空间的笛卡尔积的映射索引等于它们的\({\mathbb {Z}} /2\) -索引。本文的主要目的是研究G空间的 Hedetniemi 猜想的拓扑版本。事实上，我们证明了拓扑 Hedetniemi 猜想对于一般的G空间对是不成立的。更准确地说，我们证明，如果群G是循环p群或大小为 2 的幂的广义四元数群，则该猜想可能成立。