# Definition:Solvable Group

(Redirected from Definition:Soluble Group)

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## Contents

## 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**.

## 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