Field:F4

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 $F_{4}$ or $GF(4)$, is the unique field (up to isomorphism) with four elements. It can be defined as:

$F_{2}[x]/(x^{2}+x+1)$.

Facts

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

Related groups

Group functor	Value	GAP ID
additive group	Klein four-group	(4,2)
multiplicative group	cyclic group:Z3	(3,1)
general linear group of degree two	general linear group:GL(2,4)	(180,19)
special linear group of degree two	alternating group:A5	(60,5)
projective general linear group of degree two	alternating group:A5	(60,5)
projective special linear group of degree two	alternating group:A5	(60,5)
projective special linear group of degree three	projective special linear group:PSL(3,4)	Order 20160, no GAP ID.

GAP implementation

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

GF(4)