Groups and symmetry

1. Solve the following equations with respect to x:
a) sr^3 sr^5 x(sr)^(-1)=(r^2 s)^2            in D_6
b) (1 3 4)x(3 2)=(1 2 3 4)          in S_4

2. Determine the order of the consecutive elements:
a) x=3 in R,
b) x=4  in Z_12,
c) x=7  in R_20,
d) x=r^2 s  in D_7,
e) x=(1 2 5 7)(3 4 6 8 9 10)  in S_10
What is the order of the mentioned groups?

3. Find all subgroups of
a) Z_8,b) D_5,c) R_8,

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