论文标题
理性横截面，有限的产生和群体的订单
Rational cross-sections, bounded generation and orders on groups
论文作者
论文摘要
我们使用有界生成的连接和组对组的连接提供了无合理横截面的组的新示例（也称为常规正常形式）。具体来说，我们的例子是无限扭转组，一组Grigorchuk类型的扩展，类似于$ C_2 \ WR（C_2 \ WR \ Mathbb Z）$和$ \ Mathbb Z \ WR F_2 $，$ \ Mathbb z $的排列和一个有限的hnnnnnnnnnnnnnnnnnnnn grigor的$ c_2 \ wr \ mathbb z）$和$ \ mathbb z \ wr f_2 $类似的花环。最后一个组是有限呈现的组的第一个示例，该组具有可解决的单词问题，没有合理的横截面。它也不可自动储存，并且没有左规范的完整重写系统。
We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Specifically, our examples are extensions of infinite torsion groups, groups of Grigorchuk type, wreath products similar to $C_2\wr(C_2\wr \mathbb Z)$ and $\mathbb Z\wr F_2$, a group of permutations of $\mathbb Z$, and a finitely presented HNN extension of the first Grigorchuk group. This last group is the first example of finitely presented group with solvable word problem and without rational cross-sections. It is also not autostackable, and has no left-regular complete rewriting system.
