Math, asked by christycochin, 2 months ago

Order of the element a^2 in the multiplicative froup G = {a, a^2, ^3, g4, A5, a^6=e} is Select one: O a. 3 O b. 1 O c. 4 O d. 2 ?​

Answers

Answered by syed2020ashaels
0

The order of a^{2} in the group is 3.

  • The quantity of a finite group's elements determines its order in mathematics. If a group is infinitely large, its order is said to be infinite. The order of a group's elements, also known as period length or period, is the order of the subgroup that element created.
  • The lowest positive integer m such that a^{m} = e, where e denotes the identity element of the group and a^{m} signifies the product of m copies of a, is the order of an element an of a group if the group operation is specified as a multiplication. The order of an is limitless if there is no such thing as m.

Now, according to the given information, the multiplicative group G is defined as: { a,a^{2} ,a^{3},a^{4}  ,a^{5},a^{6} }

Now, (a^{2})^{3} is equal to a^{6} which is equal to e, that is, the identity element in the group.

Then, the order of a^{2} in the group is 3.

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