- #1

- 80

- 1

## Homework Statement

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)

## 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!