AI 中文总结
该研究构造了具有Dehn函数$n^2 \log n$的2步Carnot群，改进了Wenger的下界，得到首个幂零群中不按$n^\alpha$（$\alpha \geq 1$）增长的Dehn函数的精确计算结果。
AI 中文摘要
我们构造了具有Dehn函数$n^2 \log n$的2步Carnot群，改进了Wenger对这类群的超二次下界估计。其中部分群容许格，由此得到具有Dehn函数$n^2 \log n$的有限生成幂零群。这是幂零群，更一般地，是具有次指数Dehn函数的有限表现可解群中，首次对不按任意$\alpha \geq 1$的$n^\alpha$增长的Dehn函数进行的精确计算。
英文摘要
We exhibit 2-step Carnot groups with Dehn function $n^2 \log n$, sharpening Wenger's superquadratic lower bound for these groups. Some of these groups admit lattices, yielding finitely generated nilpotent groups with Dehn function $n^2 \log n$. This gives the first exact computation of a Dehn function which does not grow like $n^α$ for any $α\geq 1$ among nilpotent groups and, more generally, among finitely presented solvable groups with subexponential Dehn function.
Comments19 pages. Comments and suggestions are welcome!
