Field:F3

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Template:Particular field

Definition

This field, denoted F_3 or GF(3), is the unique field of three elements. It can be defined as the ring of integers modulo 3.

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 as:

GF(3)

It can also be defined using GAP's ZmodnZ function as:

ZmodnZ(3)