Decidability of Word Problem for Just Infinite Groups
Published:Dec 30, 2025 14:39
•1 min read
•ArXiv
Analysis
This paper addresses a fundamental problem in group theory: the word problem. It demonstrates that for a specific class of groups (finitely generated just infinite groups), the word problem is algorithmically decidable. This is significant because it provides a positive result for a class of groups where the word problem's decidability wasn't immediately obvious. The paper's approach, avoiding reliance on the Wilson-Grigorchuk classification, offers a potentially more direct and accessible proof.
Key Takeaways
Reference
“The word problem is algorithmically decidable for finitely generated just infinite groups given by a recursively enumerable set of relations.”