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# Order of elements in multiplicative group watch

1. Hey, does anyone know how to find the order of elements of a multiplicative group?

For example, finding the order of elements 1,2,3,4 in multiplicative group of nonzero elements of the field Z/11Z?
2. (Original post by maths10101)
Hey, does anyone know how to find the order of elements of a multiplicative group?

For example, finding the order of elements 1,2,3,4 in multiplicative group of nonzero elements of the field Z/11Z?
The order of an element is the smallest positive integer s.t: .

E.g:
4^1 = 1 neq 1 mod 11
4^2 = 16 neq 1 mod 11
4^3 = 64 neq 1 mod 11
4^4 neq 1 mod 11
4^5 = 1 mod 11, so the order is 5.
3. The order of an element in a group is the order of the subgroup generated by the element.

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