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Cyclic Groups and Primitive Roots

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

Abstract

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.

Keywords

Cyclic Group Prime Power Cyclic Subgroup Invertible Element Primitive Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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