An algebraically fibering group is an algebraic generalization of the fibered 3-manifold group in higher dimensions. Let $M(\mathcal{P})$ and $M(\mathcal{E})$ be the cusped and compact hyperbolic real moment-angled manifolds associated with the hyperbolic right-angled 24-cell $\mathcal{P}$ and the hyperbolic right-angled 120-cell $\mathcal{E}$, respectively. Jankiewicz, Norin, and Wise recently showed that ${\pi }_1(M(\mathcal{P}))$ and ${\pi }_1(M(\mathcal{E}))$ are algebraically fibered. In other words, there are two exact sequences$1\to H_{\mathcal{P}}\to {\pi }_1(M(\mathcal{P}))\stackrel{{\varphi }_{\mathcal{P}}}{\to }\mathbb{Z}\to 1,$$1\to H_{\mathcal{E}}\to {\pi }_1(M(\mathcal{E}))\stackrel{{\varphi }_{\mathcal{E}}}{\to }\mathbb{Z}\to 1,$ where $H_{\mathcal{P}}$ and $H_{\mathcal{E}}$ are finitely generated. In this paper, we further show that the fiber-kernel groups $H_{\mathcal{P}}$ and $H_{\mathcal{E}}$ are not $F{P}_2$. In particular, they are finitely generated, but not finitely presented.

代数纤维化基团是纤维状3-歧管基团在更高维度上的代数概括。让$\mathrm{中号}（\mathcal{P}）$ 和 $\mathrm{中号}（\mathcal{Ë}）$ 是与双曲直角24格关联的尖锐且紧凑的双曲实矩弯形歧管 $\mathcal{P}$ 和双曲直角120单元 $\mathcal{Ë}$， 分别。Jankiewicz，Norin和Wise最近表明${\pi }_{\mathrm{1个}}（\mathrm{中号}（\mathcal{P}））$ 和 ${\pi }_{\mathrm{1个}}（\mathrm{中号}（\mathcal{Ë}））$是代数纤维。换句话说，有两个确切的序列$\mathrm{1个}\to H_{\mathcal{P}}\to {\pi }_{\mathrm{1个}}（\mathrm{中号}（\mathcal{P}））\stackrel{{\varphi }_{\mathcal{P}}}{\to }\mathbb{ž}\to \mathrm{1个}，$$\mathrm{1个}\to H_{\mathcal{Ë}}\to {\pi }_{\mathrm{1个}}（\mathrm{中号}（\mathcal{Ë}））\stackrel{{\varphi }_{\mathcal{Ë}}}{\to }\mathbb{ž}\to \mathrm{1个}，$ 哪里 $H_{\mathcal{P}}$ 和 $H_{\mathcal{Ë}}$是有限生成的。在本文中，我们进一步证明了光纤内核组$H_{\mathcal{P}}$ 和 $H_{\mathcal{Ë}}$ 不是 $F{P}_2$。特别是，它们是有限生成的，但不是有限呈现的。