- #1
TimeRip496
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Homework Statement
What are the subgroups of Z2 x Z2 x Z2?
Homework Equations
Hint: There are 16 subgroups.
The Attempt at a Solution
So far I only manage to get 15 and I am not even sure if these are correct.
My answer: $$(0,0,0) , (Z_2,Z_2,Z_2), (1,1,1), (0,0,1), (0,1,0), (1,0,0), (0,1,1), (1,0,1), (1,1,0), (0,Z_2,Z_2), (Z_2,0,Z_2),(Z_2,Z_2,0), (1,1,Z_2), (1,Z_2,1), (Z_2,1,1)$$
where <(Z2, Z2, Z2)> is not the same as <(1,1,1)>
$$<(Z_2,Z_2,Z_2)> = {(0,0,0),(1,1,1),(0,0,1),(0,1,0),(1,0,0),(0,1,1),(1,0,1),(1,1,0)}$$
$$<(1,1,1)>={(0,0,0),(1,1,1)}$$
Forgive me as I just started group theory and I am now using videos on visual group theory as a guide. The above question comes from here.