Question: Prove the Finite Subgroup Theorem: let G be a group and H a finite non-empty subset of G. Then H is a subgroup of
Prove the Finite Subgroup Theorem: let G be a group and H a finite non-empty subset of G. Then H is a subgroup of G if and only if whenever g, h H, then gh H. Furthermore, give an example where this theorem does not hold for an infinite set H in a group G (thus, that H is finite is crucial to the theorem). [10]
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First Part Let H be a subgroup of G Since H is a group H is closed under Therefore gH hH ghH ... View full answer
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