Field:F8: Difference between revisions
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| [[projective special linear group of degree two]] || [[projective special linear group:PSL(3,2)]] || (168,42) | | [[projective special linear group of degree two]] || [[projective special linear group:PSL(3,2)]] || (168,42) | ||
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==GAP implementation== | |||
{{GAP finite field|8}} | |||
Latest revision as of 10:59, 9 December 2023
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 eight elements. It is denoted or . It can be defined as:
.
where is the field of two elements.
Related groups
| Group functor | Value | GAP ID |
|---|---|---|
| additive group | elementary abelian group:E8 | (8,5) |
| multiplicative group | cyclic group:Z7 | (7,1) |
| general affine group of degree one | general affine group:GA(1,8) | (56,11) |
| projective special linear group of degree two | projective special linear group:PSL(3,2) | (168,42) |
GAP implementation
The field can be defined using GAP's GF function:
GF(8)