# Field:F9

From Groupprops

## Definition

This is the unique field (up to isomorphism) of nine elements. It can be defined as:

where is the field of three elements.

## Related groups

Group functor | Value | Explanation |
---|---|---|

additive group | elementary abelian group:E9 | |

multiplicative group | cyclic group:Z8 | |

general affine group of degree one | general affine group:GA(1,9) | |

projective special linear group of degree two | alternating group:A6 | |

projective general linear group of degree two | projective general linear group:PGL(2,9) | |

special linear group of degree two | special linear group:SL(2,9) | |

general linear group of degree two | general linear group:GL(2,9) |

## GAP implementation

This field can be defined using GAP's GF function:

`GF(9)`