论文标题
关于广泛的共轭和一些相关问题
On generalized conjugacy and some related problems
论文作者
论文摘要
我们在$ g $ - $ - $ \ mathbb {z} $ group，$ gcp（g \ rtimes \ mathbb {z}）$之间建立了连接$ GTCP（g）$。我们探讨了不同种类的概括：相对于有限生成的亚组，与它们的cosets或该组的可识别，理性，无上下文或代数子集相对于有限生成的子组。使用此结果，我们能够证明$ GBRCP（g）$是可决定的（相对于cosets），当$ g $是一个几乎是多环形组时，这特别意味着如果$ g $是有一定的生成的艾比亚利亚集团，则可以决定普遍的Brinkmann的平等问题，即$ GBRP（g）$。最后，我们证明，如果$ g $是一个有限生成的几乎没有免费的组，那么Brinkmann的平等问题和扭曲的共轭问题的简单版本，$ brp（g）$和$ tcp（g）$是可决定的。
We establish a connection between the generalized conjugacy problem for a $G$-by-$\mathbb{Z}$ group, $GCP(G \rtimes \mathbb{Z})$, and two algorithmic problems for $G$: the generalized Brinkmann's conjugacy problem, $GBrCP(G)$, and the generalized twisted conjugacy problem, $GTCP(G)$. We explore this connection for generalizations of different kinds: relative to finitely generated subgroups, to theirs cosets, or to recognizable, rational, context-free or algebraic subsets of the group. Using this result, we are able to prove that $GBrCP(G)$ is decidable (with respect to cosets) when $G$ is a virtually polycyclic group, which implies in particular that the generalized Brinkmann's equality problem, $GBrP(G)$, is decidable if $G$ is a finitely generated abelian group. Finally, we prove that if $G$ is a finitely generated virtually free group, then the simple versions of Brinkmann's equality problem and of the twisted conjugacy problem, $BrP(G)$ and $TCP(G)$, are decidable.
