Field:F4
From Groupprops
Definition
This field, denoted or
, is the unique field (up to isomorphism) with four elements. It can be defined as:
.
Facts
- For any natural number
, 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. |