I've learned about generate a group by a set. I saw some examples of infinite group and finite group that generated by a set. But I come up with a question: is there any conditions or theorems that show us a set can generate a finite group?
2026-03-25 07:43:16.1774424596
How can we generate a finite group by a set?
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If you talk about the group presentation, you have for exemple : $$\mathbb{Z}/2\mathbb{Z} = <\{x\};{x^2=1}>.$$ Your set represent the generators of your group, and then you add some relations to these elements. If you have enough relations (torsion), your group is finite.