标题： 晶体学 Helly 群 显示英文标题

标题： Crystallographic Helly Groups

摘要： 我们证明了Helly图的渐近锥是可数超凸的。 我们利用这一点来证明虚拟幂零的Helly群是虚拟阿贝尔的，并通过它们的点群来表征虚拟阿贝尔的Helly群。 事实上，我们对更一般的粗略内射空间和群进行了这些工作。 我们应用这一点来证明$3$-$3$-$3$-Coxeter群不是Helly的（甚至不是粗略内射的），从而得到了第一个不是Helly的系统群的例子，回答了Chalopin、Chepoi、Genevois、Hirai和Osajda提出的问题。 显示英文摘要

摘要： We prove that asymptotic cones of Helly graphs are countably hyperconvex. We use this to show that virtually nilpotent Helly groups are virtually abelian and to characterize virtually abelian Helly groups via their point groups. In fact, we do this for the more general class of coarsely injective spaces and groups. We apply this to prove that the $3$-$3$-$3$-Coxeter group is not Helly (nor even coarsely injective), thus obtaining the first example of a systolic group that is not Helly, answering a question of Chalopin, Chepoi, Genevois, Hirai, and Osajda.