Primitive element

In field theory, a primitive element of a finite field GF(q) is a generator of the multiplicative group of the field. In other words, is called a primitive element if all the non-zero elements of GF(q) can be written as αⁱ for some (positive) integer i.

For example, 2 is a primitive element of the field GF(3) and GF(5), but not of GF(7) since it generates the cyclic subgroup of order 3 {2,4,1}; however, 3 is a primitive element of GF(7). The minimal polynomial of a primitive element is a primitive polynomial.

See also

• Primitive element (field theory)
• Primitive root

References

• Lidl, Rudolf; Harald Niederreiter (1997). Finite Fields (2nd ed.). Cambridge University Press. ISBN 0-521-39231-4. 

External links

• Weisstein, Eric W., "Primitive Polynomial" from MathWorld.

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