7. Suppose G is a finite group and let n be a factor of |G|. Suppose N≤ G is the only subgroup of G of size n. Prove that N is a normal subgroup of G.

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7.
Suppose G is a finite group and let ʼn be a factor of |G|.
Suppose N≤ G is the only subgroup of G of size n. Prove that N is a
normal subgroup of G.
Transcribed Image Text:7. Suppose G is a finite group and let ʼn be a factor of |G|. Suppose N≤ G is the only subgroup of G of size n. Prove that N is a normal subgroup of G.
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