论文标题
具有二次DEHN功能的组的扭转亚组
Torsion Subgroups of Groups with Quadratic Dehn Function
论文作者
论文摘要
我们构建具有有限生成的无限扭转亚组的有限分组的第一个示例。这些示例是“最佳”的，因为任何有限提出的组的dehn函数至少必须是二次的。此外，我们表明，对于任何$ n \ geq2^{48} $，$ n $是奇怪的或可分开的$ 2^9 $，任何带有指数$ n $的无限自由伯恩赛组都是一个准嵌入的子组，该组有一个有限端的子组具有Quadratic Dehn功能的Quadratic Dehn函数的函数，可满足象征性的扩展。
We construct the first examples of finitely presented groups with quadratic Dehn function containing a finitely generated infinite torsion subgroup. These examples are "optimal" in the sense that the Dehn function of any such finitely presented group must be at least quadratic. Moreover, we show that for any $n\geq2^{48}$ such that $n$ is either odd or divisible by $2^9$, any infinite free Burnside group with exponent $n$ is a quasi-isometrically embedded subgroup of a finitely presented group with quadratic Dehn function satisfying the Congruence Extension Property.
