Field:F9

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Template:Particular field

Definition

This is the unique field (up to isomorphism) of nine elements. It can be defined as:

F_3[x]/(x^2 + 1)

where F_3 is the field of three elements.

Related groups

Group functor Value Explanation
additive group elementary abelian group:E9
multiplicative group cyclic group:Z8
general affine group of degree one general affine group:GA(1,9)
projective special linear group of degree two alternating group:A6
projective general linear group of degree two projective general linear group:PGL(2,9)
special linear group of degree two special linear group:SL(2,9)
general linear group of degree two general linear group:GL(2,9)

GAP implementation

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

GF(9)