Definition:Solvable Group

Definition

Let $G$ be a finite group.

Then $G$ is a solvable group if and only if it has a composition series in which each factor is a cyclic group.

Also known as

A solvable group is also known as a soluble group.

Examples

Symmetry Group of Equilateral Triangle is Solvable

Symmetry Group of Equilateral Triangle is Solvable

Also see

• Results about solvable groups can be found here.

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Normal and Composition Series: $\S 75$. Solvable Groups
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): soluble group (US: solvable group)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): soluble group (US: solvable group)