Field:F9
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) of nine elements. It can be defined as:
![{\displaystyle F_{3}[x]/(x^{2}+1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf96404a452a017cacdedbcca3f885690e67874f)
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
The field can be defined using GAP's GF function:
GF(9)