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arXiv · 1905.04892

A Hales--Jewett type property of finite solvable groups

Vassilis Kanellopoulos·Miltiadis Karamanlis
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Abstract

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 Kříž in Euclidean Ramsey theory.

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Vassilis Kanellopoulos, Miltiadis Karamanlis. 2019-05-13. A Hales--Jewett type property of finite solvable groups. https://arxiv.org/abs/1905.04892

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