# Definition:Hamiltonian Group

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## Contents

## Definition

A group $G$ is described as **Hamiltonian** if and only if $G$ is a non-abelian group such that every subgroup is normal.

## Also see

- Results about
**Hamiltonian groups**can be found here.

## Source of Name

This entry was named for William Rowan Hamilton.

## Sources

- 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): Chapter $2$: Conjugacy, Normal Subgroups, and Quotient Groups: $\S 46 \iota$