Field:F11
This article is about a particular field, i.e., a field unique up to isomorphism. View a complete list of particular fields
Definition
This is the unique field (up to isomorphism) having eleven elements. It is a prime field, and is the quotient of the ring of integers by the ideal of multiples of .
Related groups
| Group functor | Value | GAP ID |
|---|---|---|
| additive group | cyclic group:Z11 | (11,1) |
| multiplicative group | cyclic group:Z10 | (10,2) |
| general affine group of degree one | general affine group:GA(1,11) | (110,1) |
| general linear group of degree two | general linear group:GL(2,11) | |
| special linear group of degree two | special linear group:SL(2,11) | (1320,13) |
| projective general linear group of degree two | projective general linear group:PGL(2,11) | (1320,133) |
| projective special linear group of degree two | projective special linear group:PSL(2,11) | (660,13) |
GAP implementation
The field can be defined using GAP's GF function:
GF(11)
It can also be defined using the ZmodnZ function:
ZmodnZ(11)