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Let G be a group such that |G| = 1000. Show that G has a proper, nontrivial normal subgroup. Let G be a group such

Let G be a group such that |G| = 1000. Show that G has a proper, nontrivial normal subgroup.

Let G be a group such that |G| = 30. Show that G has a proper, nontrivial normal subgroup.

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