Field:F2

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Template:Particular field

Definition

This field, denoted F_2 or GF(2), is the unique field (up to isomorphism) of two elements.

Facts

Related groups

Group functor Value GAP ID
additive group cyclic group:Z2 (2,1)
multiplicative group trivial group (1,1)
general affine group of degree one cyclic group:Z2 (2,1)
general linear group of degree two symmetric group:S3 (6,1)
special linear group of degree two symmetric group:S3 (6,1)
projective general linear group of degree two symmetric group:S3 (6,1)
projective special linear group of degree two symmetric group:S3 (6,1)
outer linear group of degree two direct product of S3 and Z2 (12,4)
general affine group of degree two symmetric group:S4 (24,12)
projective special linear group of degree three projective special linear group:PSL(3,2) (168,42)
projective special linear group of degree four alternating group:A8 The order is 20160, no GAP ID.

GAP implementation

The field can be defined using GAP's GF function as:

GF(2)

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

ZmodnZ(2)