A conjecture of Leader, Russell and Walters in Euclidean Ramsey theory says that a finite set is Ramsey if and only if it is congruent to a subset of a set whose symmetry group acts transitively. As they have shown the ``if" direction of their conjecture follows if all finite groups have a Hales--Jewett type property. In this paper, we show that this property is satisfied in the case of finite solvable groups. Our result can be used to recover the work of Křiž in Euclidean Ramsey theory.

中文翻译：

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有限可解群的 HALES-JEWETT 型性质

Leader、Russell 和 Walters 在欧几里得拉姆齐理论中的一个猜想说，有限集是拉姆齐当且仅当它与对称群传递性作用的集合的子集全等。正如他们已经表明，如果所有有限群都具有 Hales--Jewett 型性质，则他们的猜想的“if”方向如下。在本文中，我们证明了在有限可解群的情况下该性质是满足的。我们的结果可以是用于恢复 Křiž 在欧几里得拉姆齐理论中的工作。