The question is:
Can every finite group G be presented by a finite set of generators and a finite set of relations?
I think the answer is yes, but I can't find a general way to decompose every finite groups into generators and relations.
2026-03-27 16:26:08.1774628768
Is every finite group finitely presented? (From Michael Artin's book)
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The answer is indeed yes: Consider the finite set of relations $$R:=\{g_1g_2g_3^{-1}\mid (g_1g_2=g_3)(g_1,g_2,g_3\in G)\}.$$ Then $\langle G\mid R\rangle$ is a presentation of $G$ with a finite set of generators $G$, and a finite set of relations $R$.