论文标题
有关组和反击自动机的更多信息
More on Groups and Counter Automata
论文作者
论文摘要
长老，kambites和Ostheimer表明，如果有限生成的$ h $的问题被$ g $ -Automaton接受了Abelian Group $ G $，那么$ H $实际上是Abelian。我们为定理提供了新的，基础和纯粹的组合证明。此外，我们的方法从自动机中提取了两组$ g $和$ h $之间的明确连接，作为$ g $的子组的组同构，以$ g $的子组为$ h $的有限索引子组。
Elder, Kambites, and Ostheimer showed that if the word problem of a finitely generated group $H$ is accepted by a $G$-automaton for an abelian group $G$, then $H$ is virtually abelian. We give a new, elementary, and purely combinatorial proof to the theorem. Furthermore, our method extracts an explicit connection between the two groups $G$ and $H$ from the automaton as a group homomorphism from a subgroup of $G$ onto a finite index subgroup of $H$.
