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Question

A cyclic group O(G)=200 g be its generator O(g^x)=100 for some x.what is value of x?

a.1

b.2

c.3

d.4

1 and 3 cant be possible as [order of generator equal to order of group] how to choose bw 2 and 4???

Answer 1

Formulae for the order of generator for a cyclic group is: O(g^x) = O(G) / [ GCD(O(G) , x) ]

In the given question,

x=? , O(G) = 200, O(g^x) = 100.

100 = 200 / GCD(200, x) -->  GCD(200,x) = 2   --> x = 2.

So the O(g^x) = 2.

Comments

how this formula came?Any Ref

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Assume there are 6 elements in a cyclic group {a^0,a^1,a^2,a^3,a^4,a^5}. Here, all elements are generators.

let's find O[(a^1)^2], it will generate {a^2,a^4,a^0,a^2,a^4....} set of elements with order 3.. which is 6/GCD(6,2).

let me know if anything is unclear..

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@Abhisek Tiwari 4

https://gateoverflow.in/250931/cyclic-group