论文标题
投影小组的基本多面体
Fundamental polyhedra of projective elementary groups
论文作者
论文摘要
对于$ o $一个假想的二次戒指，我们计算了$ \ text {pe} _2（o）$的基本多面体，$ \ text {psl} _2（o）$的投射基本亚组。这允许新的，简化的Cohn，Nica，Fine和Frohman定理的证据。也就是说，我们获得了$ \ text {pe} _2（o）$的演示文稿，表明它具有无限索引，并且是其自己的归一化为$ \ text {psl} _2（o）$，并拆分$ \ text {psl} {psl} _2（o）_2（o）_2（o）$ a imalgamation $ a} $} $}（o）o} o}。
For $O$ an imaginary quadratic ring, we compute a fundamental polyhedron of $\text{PE}_2(O)$, the projective elementary subgroup of $\text{PSL}_2(O)$. This allows for new, simplified proofs of theorems of Cohn, Nica, Fine, and Frohman. Namely, we obtain a presentation for $\text{PE}_2(O)$, show that it has infinite-index and is its own normalizer in $\text{PSL}_2(O)$, and split $\text{PSL}_2(O)$ into a free product with amalgamation that has $\text{PE}_2(O)$ as one of its factors.
