Field:F2

This article is about a particular field, i.e., a field unique up to isomorphism. View a complete list of particular fields

Definition

This field, denoted $F_{2}$ or $GF(2)$, is the unique field (up to isomorphism) of two elements.

Facts

• For any natural number $n$, the projective general linear group, projective special linear group, special linear group, and general linear group are all the same.

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:

GF(2)

It can also be defined using the ZmodnZ function:

ZmodnZ(2)