Prove that the subgroup {o E S | o (5) = 5} of Sg is isomorphic to S4.
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- 9. Suppose that and are subgroups of the abelian group such that . Prove that .5. For any subgroup of the group , let denote the product as defined in Definition 4.10. Prove that corollary 4.19:11. Assume that are subgroups of the abelian group such that the sum is direct. If is a subgroup of for prove that is a direct sum.