9. Let T be a subset of a group (G, o, e). Show that (T) equals the

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9. Let T be a subset of a group (G, o, e). Show that (T) equals the intersection of all subgroups of G that contain T. Thus, (T) in Definition 2.31 is indeed well-defined.

Prove Fermat's theorem (Theorem 2.15). Consider the group

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