# Field:F4

From Groupprops

## Definition

This field, denoted or , is the unique field (up to isomorphism) with four elements. It can be defined as:

.

## Facts

- For any natural number , the projective special linear group, special linear group and projective general linear group are isomorphic.

## Related groups

Group functor | Value | GAP ID |
---|---|---|

additive group | Klein four-group | (4,2) |

multiplicative group | cyclic group:Z3 | (3,1) |

general linear group of degree two | general linear group:GL(2,4) | (180,19) |

special linear group of degree two | alternating group:A5 | (60,5) |

projective general linear group of degree two | alternating group:A5 | (60,5) |

projective special linear group of degree two | alternating group:A5 | (60,5) |

projective special linear group of degree three | projective special linear group:PSL(3,4) | Order 20160, no GAP ID. |