Year: 2026
Type: preprint
Abstract: We prove that nilpotent and metabelian products of groups with decidable word problem have decidable word problem. In contrast, we exhibit families of groups with decidable word problem for which their solvable product have undecidable word problem. In doing so, we exhibit hyperbolic groups with undecidable membership problem in its derived subgroups.
Source: arXiv (Cornell University)
Authors: Brude, Javier, Sasyk, Román
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214585397