https://en.wikipedia.org/wiki/Multiplicative_group Multiplicative group (抜粋) 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}.
