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