## Characteristic Factor

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.

See also Cyclic Group, Direct Product (Group), Modulo Multiplication Group, Totient Function

References

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