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How do we start this proof? (a) Let x  gHg -1. (b)  (c) Assume a, b  H (d) Show Nonempty:

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Presentation on theme: "How do we start this proof? (a) Let x  gHg -1. (b)  (c) Assume a, b  H (d) Show Nonempty:"— Presentation transcript:

1 How do we start this proof? (a) Let x  gHg -1. (b)  (c) Assume a, b  H (d) Show Nonempty:

2 What is the next line of the proof? (a) Assume H is normal. (b) Assume ab -1  H (c) Assume a, b  H (d) Assume if ab -1  H then Ha = Hb.

3 What is the next line of the proof? (a) Assume gHg -1 = H (b) Let x  gHg -1 (c) Assume g  H (d) Assume gHg -1 = H.

4 What is the next line of the proof? (a) Assume gHg -1 = H (b) Let x  gHg -1 (c) Let h  H (d) Assume gHg -1 = H.

5 What is the next line of the proof? (a) Assume gHg -1 = H (b) Let x  gHg -1 (c) Let ghg -1 = h (d) Let H be a subgroup.

6 What is the next line of the proof? (a) Assume H is normal. (b) Assume H is abelian. (c) Let g  G, h  H. (d) Let gHg -1 = H.

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