Field:F3
This article is about a particular field, i.e., a field unique up to isomorphism. View a complete list of particular fields
Definition
This field, denoted or , is the unique field of three elements. It can be defined as the ring of integers modulo .
Related groups
| Group functor | Value | GAP ID |
|---|---|---|
| additive group | cyclic group:Z3 | (3,1) |
| multiplicative group | cyclic group:Z2 | (2,1) |
| general affine group of degree one | symmetric group:S3 | (6,1) |
| general linear group of degree two | general linear group:GL(2,3) | (48,29) |
| special linear group of degree two | special linear group:SL(2,3) | (24,3) |
| projective general linear group of degree two | symmetric group:S4 | (24,12) |
| projective special linear group of degree two | alternating group:A4 | (12,3) |
| projective special linear group of degree three | projective special linear group:PSL(3,3) | order 5616, no GAP ID. |
| upper-triangular unipotent matrix group of degree three | prime-cube order group:U(3,3) | (27,3) |
GAP implementation
The field can be defined using GAP's GF function:
GF(3)
It can also be defined using the ZmodnZ function:
ZmodnZ(3)