论文标题
Brin-Higman-Thompson组的单词问题
The word problem of the Brin-Higman-Thompson groups
论文作者
论文摘要
我们表明，Brin-higman-Thompson组的单词问题$ n g_ {k，1} $ is {\ sf conp} -complete for All $ n \ ge 2 $和所有$ k \ ge 2 $。为此，我们证明$ n g_ {k，1} $是有限生成的，并且$ n g_ {k，1} $包含一个可以代表生物电路的$ 2 g_ {2,1} $的子组。 我们还表明，对于所有$ n \ ge 1 $和$ k \ ge 2 $：\如果$ \，k = 1 +（k-1）\，n \，$，对于某些$ n \ ge 1 $，然后$ n g_ {k，1} \ le n g_ g_ {k {k，1} $。特别是，$ n g_ {k，1} \ le n g_ {2,1} $ for All $ k \ ge 2 $。
We show that the word problem of the Brin-Higman-Thompson group $n G_{k,1}$ is {\sf coNP}-complete for all $n \ge 2$ and all $k \ge 2$. For this we prove that $n G_{k,1}$ is finitely generated, and that $n G_{k,1}$ contains a subgroup of $2 G_{2,1}$ that can represent bijective circuits. We also show that for all $n \ge 1$ and $k \ge 2$: \ If $\,K = 1 + (k-1)\,N\,$ for some $N \ge 1$, then $n G_{K,1} \le n G_{k,1}$. In particular, $n G_{K,1} \le n G_{2,1}$ for all $K \ge 2$.
