Field:F7
This article is about a particular field, i.e., a field unique up to isomorphism. View a complete list of particular fields
Definition
This is the unique field (up to isomorphism) having seven elements. It is a prime field, and is the quotient of the ring of integers by the ideal of multiples of .
Related groups
| Group functor | Value | GAP ID |
|---|---|---|
| additive group | cyclic group:Z7 | (7,1) |
| multiplicative group | cyclic group:Z6 | (6,2) |
| general affine group of degree one | general affine group:GA(1,7) | (42,1) |
| general linear group of degree two | general linear group:GL(2,7) | |
| special linear group of degree two | special linear group:SL(2,7) | (336,114) |
| projective general linear group of degree two | projective general linear group:PGL(2,7) | (336,208) |
| projective special linear group of degree two | projective special linear group:PSL(2,7) | (168,42) |
GAP implementation
The field can be defined using GAP's GF function:
GF(7)
It can also be defined using the ZmodnZ function:
ZmodnZ(7)