Every Finite Group Admits a Just Finite Presentation

Mathematician Marc Lackenby has resolved a long-standing open question in group theory, specifically Problem 21.10 from the Kourovka Notebook. The research confirms that every finite group admits a 'just finite' presentation. A finite presentation of a group is defined as 'just finite' if the removal of any single relation from its set of relations results in a presentation for an infinite group. This property ensures that the finiteness of the group is critically dependent on every relation in the presentation. By resolving this conjecture in the affirmative, Lackenby provides a significant theoretical advancement in the understanding of finite group structures and their presentations. The paper, submitted to arXiv under the Mathematics > Group Theory category, contributes to the foundational knowledge of algebraic structures. This result settles a specific problem that had remained unsolved in the mathematical community, offering new insights into the minimal conditions required to define finite groups through generators and relations.