A characteristic factor is a factor in a particular factorization of the Totient Function such that the product of characteristic factors gives the representation of a corresponding abstract Group as a Direct Product. By computing the characteristic factors, any Abelian Group can be expressed as a Direct Product of Cyclic Subgroups, for example, Finite Group Z2Z4 or Finite Group Z2Z2Z2. There is a simple algorithm for determining the characteristic factors of Modulo Multiplication Groups.

**References**

Shanks, D. *Solved and Unsolved Problems in Number Theory, 4th ed.* New York: Chelsea, p. 94, 1993.

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1999-05-26