Cyclic Groups and Primitive Roots
The fact that there is a primitive root modulo p means that the group of invertible elements of ℤ /pℤ is a cyclic group. In this chapter we examine cyclic groups, and then ask, for which m is the group of units of ℤ/mℤ a cyclic group. To answer this question for m a prime power, we use the primary decomposition theorem for finite abelian groups.
KeywordsCyclic Group Prime Power Cyclic Subgroup Invertible Element Primitive Element
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