Solvable Groups

Relevant Classes: Math 493.

Also Known As Soluble.

Definition: Solvable Group

A group $G$ is said to be solvable if it admits a normal series in which each subquotient $G_{i+1}/G_i$ is abelian.

Remark: all Abelian Groups are solvable.

Equivalent Definition (Finite Group)

A finite group $G$ is said to be solvable if and only if the composition factors are all $C_p$ (finite cyclic groups of a prime order).