Determine the order of the consecutive elements

Reference no: EM13937924

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,
and give reasons that you have found all.

Reference no: EM13937924

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