Field:F4

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Template:Particular field

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

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.