Field:F5
From Groupprops
Definition
This is the unique field (up to isomorphism) having five 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:Z5 | (5,1) |
| multiplicative group | cyclic group:Z4 | (4,1) |
| general affine group of degree one | general affine group:GA(1,5) | (20,3) |
| general linear group of degree two | general linear group:GL(2,5) | (480,218) |
| special linear group of degree two | special linear group:SL(2,5) | (120,5) |
| projective general linear group of degree two | symmetric group:S5 | (120,34) |
| projective special linear group of degree two | alternating group:A5 | (60,5) |
GAP implementation
The field can be defined using GAP's GF function:
GF(5)
It can also be defined using the ZmodnZ function:
ZmodnZ(5)
