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# 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 group direct product. By computing the characteristic factors, any Abelian group can be expressed as a group direct product of cyclic subgroups, for example, the finite group C2×C4 or the finite group C2×C2×C2. There is a simple algorithm for determining the characteristic factors of modulo multiplication groups.

Cyclic Group, Group Direct Product, Modulo Multiplication Group, Totient Function

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## References

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

## Referenced on Wolfram|Alpha

Characteristic Factor

## Cite this as:

Weisstein, Eric W. "Characteristic Factor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CharacteristicFactor.html