Cyclic Groups and Primitive Roots

  • Lindsay N. Childs
Part of the Undergraduate Texts in Mathematics book series (UTM)


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.


Cyclic Group Prime Power Cyclic Subgroup Invertible Element Primitive Element 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Lindsay N. Childs
    • 1
  1. 1.Department of MathematicsSUNY at AlbanyAlbanyUSA

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