Definition:Primitive Element of Cyclic Modulo Group

This page is about primitive element of cyclic modulo group. For other uses, see Primitive Element.

Definition

Let $p$ be a prime number.

Let $\Z'_p$ denote the cyclic multiplicative group of reduced residues of order $p - 1$.

Let $a$ be a generator of $\Z'_p$.

Then $a$ is known as a primitive element of $\Z'_p$.

Examples

Modulo $7$

Consider the multiplicative group of reduced residues $\Z'_p$.

The elements $\eqclass 3 7$ and $\eqclass 5 7$ are the primitive elements of $\Z'_p$.

Also see

• Results about primitive elements of cyclic modulo groups can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): primitive element