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arXiv 2410.067512024-10math.GR

图积中的正向洛克斯多形

Short positive loxodromics in graph products

Elia Fioravanti, Alice Kerr

备注：: 47 pages. Minor changes in response to referee comments. Final version to appear in Groups, Geometry, and Dynamics

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AI总结：

本文提出利用正词生成图积子群中的广义洛克斯多形的方法，揭示了子群的生长特性，证明了图积的生长性质继承性。

摘要：

我们提供了一种有效生成图积子群中广义洛克斯多形的方法，利用正词。这在这些群的子集生长性方面有多种后果。特别是，我们证明具有强乘积集生长性质的图积也共享这些性质。此外，我们还证明了任何图积中某一类子群的生长速率集合是良序的。

英文摘要：

We give a method for effectively generating generalised loxodromics in subgroups of graph products, using positive words. This has several consequences for the growth of subsets of these groups. In particular, we show that graph products of groups with strong product set growth properties also share those properties. We additionally show that the set of growth rates of a class of subgroups of any graph product of equationally noetherian groups is well-ordered.

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