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.
Characteristic Factor
See also
Cyclic Group, Group Direct Product, Modulo Multiplication Group, Totient FunctionExplore with Wolfram|Alpha
References
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 94, 1993.Referenced on Wolfram|Alpha
Characteristic FactorCite this as:
Weisstein, Eric W. "Characteristic Factor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CharacteristicFactor.html