The discussion centers on the existence of groups that are finitely generated but cannot be presented with finitely many relations. A specific example mentioned is a group referenced in the paper "A finitely generated, infinitely related group with trivial multiplicator." The participants confirm that such groups do exist and inquire about their characteristics, emphasizing the interest in identifying "nice" groups within this category. The conversation highlights the complexity and intriguing nature of finitely generated groups with infinite relations.
PREREQUISITESThis discussion is beneficial for mathematicians, particularly those specializing in group theory, algebraists, and students seeking to deepen their understanding of finitely generated groups and their presentations.
markiv said:What's an example of a group that has finitely many generators, but cannot be presented using only finitely many relations? Are there any nice groups? They do exist, right?