# General affine group:GA(1,Q)

From Groupprops

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Definition

This group, denoted or , is defined in the following equivalent ways:

- It is the general affine group of degree one over the field of rational numbers . Explicitly, it is the group of transformations of the form , where , with multiplication defined by composition.
- It is the holomorph of the (additive) group of rational numbers.
- It is the external semidirect product where the latter acts on the former by multiplication.

## Group properties

Property | Satisfied? | Explanation |
---|---|---|

abelian group | No | |

finitely generated group | No | |

nilpotent group | No | |

metabelian group | Yes | |

solvable group | Yes |