Field:F8

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Template:Particular field

Definition

This is the unique field (up to isomorphism) having eight elements. It is denoted F_8 or GF(8). It can be defined as:

\! F_2[x]/(x^3 + x + 1).

where F_2 is the field of two elements.

Related groups

Group functor Value GAP ID
additive group elementary abelian group:E8 (8,5)
multiplicative group cyclic group:Z7 (7,1)
general affine group of degree one general affine group:GA(1,8) (56,11)
projective special linear group of degree two projective special linear group:PSL(3,2) (168,42)

GAP implementation

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

GF(8)