Definition:Solvable Group
(Redirected from Definition:Soluble Group)
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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)