abstract algebra HW: Let G = S_4, X = {1, 2, 3, 4}, X is a G-set. Give G_2, G_4, and

[Xekoroth]

Exercise 13.2.14. Let G = S₄ (the permutations of four elements), and let X = {1, 2, 3, 4}. X is a G-set.

. . .a. Give G₂, G₄, and \(\displaystyle G_2\, \cap\, G_4.\)
. . .Is \(\displaystyle G_2\, \cap\, G_4\) a group?
. . .Explain your answer.

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I attached the image for reference. Specifically what's confusing to me is what is meant by the notate G_2, G_4 etc.

 

[Deleted member 4993]

Exercise 13.2.14. Let G = S₄ (the permutations of four elements), and let X = {1, 2, 3, 4}. X is a G-set.

. . .a. Give G₂, G₄, and \(\displaystyle G_2\, \cap\, G_4.\)
. . . . .Is \(\displaystyle G_2\, \cap\, G_4\) a group?
. . . . .Explain your answer.

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I attached the image for reference. Specifically what's confusing to me is what is meant by the notate G_2, G_4 etc.

What are your thoughts?

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