Every finite group admits a just finite presentation
arXiv:2605.1040299.5
AI Analysis
Resolves an open conjecture in combinatorial group theory about finite group presentations.
The authors prove that every finite group has a 'just finite' presentation, where removing any relation yields an infinite group, resolving a long-standing open problem.
A finite presentation < X | R > of a finite group is called `just finite' if removing any relation from R results in a presentation for an infinite group. It has been an open question (Kourovka Notebook, Problem 21.10) whether every finite group admits such a presentation. We resolve this conjecture in the affirmative.