Let G be a group and let H be a subgroup of G. For each g E G, we define the subset gHg- of G by 9H9¬1 = {ghg¬1 | h e H}. (a) Prove that gHg¬l is a subgroup of G for every g E G.

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Q: 3. Let G be a group of order 8 that is not cyclic. Show that at = e for every a e G.

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Q: 5. Let G be a group and let H be a subgroup of G. For each g e G, we define the subset gHg-1 of G by…

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Q: Let G be a group and let a e G. In the special case when A= {a},we write Cda) instead of CG({a}) for…

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Q: 4. Let G be a group of order 49. Prove that G is cyclic or g7 = e for all g € G.

A: Given a group of order 49, then to prove that either G is cyclic or g7=e for all g∈G.

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