It is well known that any group is a homomorphic image of a free group. I want to know more about this theorem when $G$ is a finite simple group. Does there exist any reference to state about it? Thanks in advance!
2026-03-25 16:05:18.1774454718
finite simple groups and free groups
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Based on the comment you added to your question, one relationship is that any group that is generated by $k$ elements is a homomorphic image of a free group of rank $k$. This is an immediate consequence of the universal property for free groups.