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

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

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

3. What is the next line of the proof? • Assume gHg-1 = H • Let x  gHg-1 • Assume g  H • Assume gHg-1 = H.

4. What is the next line of the proof? • Assume gHg-1 = H • Let x  gHg-1 • Let h  H • Assume gHg-1 = H.

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

6. What is the next line of the proof? • Assume H is normal. • Assume H is abelian. • Let g  G, h  H. • Let gHg-1 = H.