Cyclic groups
1. The problem statement, all variables and given/known data
A. Let g = 20 in a group G. Compute g^2, g^8,g^5, g^3 B. In each case find the subgroup H = <x,y> of G. a) G = <a> is cyclic, x = a^m, y = a^k, gcd(m,k)=d b) G=S_3, x=(1 2), y=(2 3) c) G = <a> * <b>, a = 4, b = 6, x = (a^2, b), y = (a,b^3) 3. The attempt at a solution A. I know g^2 = 20/2 = 10 and g^5 = 20/5 = 4 But g^8, g^3 don't know.. B. a)H=<a^d> , right? but I don't know how to solve b) and c) Thanks! 
Re: Cyclic groups
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Re: Cyclic groups
The least common multiple of 20 and 8 is 2*4*5= 40. [itex](g^8)^5= (g^20)^2= e[/itex].
The least common multiple of 3 and 20 is 60. [itex](g^3)^20= (g^20)^3= e[/itex]. 
Re: Cyclic groups
so.. for b) is H=(1 2) * (2 3) = (1 2 3)..?

Re: Cyclic groups
Yes, that's right.

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