关于共生级数为有理级数对角线的群
On groups whose cogrowth series is the diagonal of a rational series
摘要：
我们证明了如果一个群包含$\mathbb{Z}^n \times F_m$作为有限指数子群，那么它的共生级数是每个生成集的一个有理函数的对角线。这回答了Pak和Soukup关于虚阿贝尔群的共生的一个问题，并推广了Elder、Rechnitzer、Janse van Rensburg和Wong关于Baumslag-Solitar群$\mathrm{BS}(N,N)$的共生序列的一个结果。
英文摘要：
We show that if a group contains $\mathbb{Z}^n \times F_m$ as a finite-index subgroup, then its cogrowth series is the diagonal of a rational function for every generating set. This answers a question of Pak and Soukup on the cogrowth of virtually abelian groups; and generalises a result by Elder, Rechnitzer, Janse van Rensburg, and Wong on the cogrowth series of the Baumslag-Solitar groups $\mathrm{BS}(N,N)$.
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