A characteristic factor is a factor in a particular factorization of the totient function ϕ(n) 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 C_2×C_4 or the finite group C_2×C_2×C_2. There is a simple algorithm for determining the characteristic factors of modulo multiplication groups.
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