论文标题
nilpotent ofter的代数和算术特性
Algebraic and arithmetic properties of the cogrowth sequence of nilpotent groups
论文作者
论文摘要
我们证明，在Unitriangular群体UT $（m，\ bbb z）$中，cogrowth序列的一致性是不可决定的。这与Abelian群体相反，Abelian群体的一致性是可以决定的。作为一种应用，我们得出的结论是，没有算法将cogrowth序列作为理性函数的对角线。
We prove that congruences of the cogrowth sequence in a unitriangular group UT$(m, \Bbb Z)$ are undecidable. This is in contrast with abelian groups, where the congruences of the cogrowth sequence are decidable. As an application, we conclude that there is no algorithm to present the cogrowth series as the diagonal of a rational function.
