Group Theory Basics Quiz

• A simple group is a group that is commutative
• A simple group is a group that has no proper nontrivial normal subgroups (correct)
• A simple group is a group that has only one element
• A simple group is a group that has exactly two subgroups

• The Class Equation states that every element in a group belongs to multiple conjugacy classes
• The Class Equation states that every element in a group belongs to the same conjugacy class
• The Class Equation states that there are no conjugacy classes in a group
• The Class Equation states that every element in a group belongs to a unique conjugacy class (correct)

• A normal subgroup is a subgroup that is necessarily of prime order
• A normal subgroup is a subgroup that is closed under conjugation by elements of the group (correct)
• A normal subgroup is a subgroup that contains only the identity element
• A normal subgroup is a subgroup that is not closed under conjugation by elements of the group