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https://en.wikipedia.org/wiki/Multiplicative_group
Multiplicative group
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In mathematics and group theory, the term multiplicative group refers to one of the following concepts:
・the group under multiplication of the invertible elements of a field,[1] ring, or other structure for which one of its operations is referred to as multiplication.
　In the case of a field F, the group is (F ? {0}, ?), where 0 refers to theZero element of F and the binary operation ? is the field multiplication,
・the algebraic torus GL(1).

Examples
・The multiplicative group of integers modulo n is the group under multiplication of the invertible elements of Z/nZ . When n is not prime, there are elements other thanZero that are not invertible.
・The multiplicative group of a field F}F is the set of all nonzero elements: F^x=F-{0}, under the multiplication operation.
　If F is finite of order q (for example q = p a prime, and F= Fp=Z/pZ), then the multiplicative group is cyclic: F^x ＝〜 C_{q-1}.

Group scheme of roots of unity
The group scheme of n-th roots of unity is by definition the kernel of the n-power map on the multiplicative group GL(1), considered as a group scheme.

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