2022/11/18 by Carvalho, André · 1 citation
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2211.10386
We establish a connection between the generalized conjugacy problem for a G-by-ℤ group, GCP(G \rtimes 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.