Solvable and Nilpotent Groups

Definition of Commutator

Derived Subgroup

Properties of Derived Subgroups

Definition of Solvable Group

Derived Series

Solvable Length

Examples of Solvable Groups

Properties of Solvable Groups

Definition of Nilpotent Group

Lower Central Series

Upper Central Series

Nilpotency Class

Examples of Nilpotent Groups

Properties of Nilpotent Groups

Nilpotent Implies Solvable

p-Groups are Nilpotent

Finite Nilpotent Groups