Field:F5

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Template:Particular field

Definition

This is the unique field (up to isomorphism) having five elements. It is a prime field, and is the quotient of the ring of integers by the ideal of multiples of 5.

Related groups

Group functor Value GAP ID
additive group cyclic group:Z5 (5,1)
multiplicative group cyclic group:Z4 (4,1)
general affine group of degree one general affine group:GA(1,5) (20,3)
general linear group of degree two general linear group:GL(2,5) (480,218)
special linear group of degree two special linear group:SL(2,5) (120,5)
projective general linear group of degree two symmetric group:S5 (120,34)
projective special linear group of degree two alternating group:A5 (60,5)

GAP implementation

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

GF(5)

It can also be defined using the ZmodnZ function:

ZmodnZ(5)