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mariab89
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Homework Statement
(a) How many distinct cyclic subgroups of D6 are there? Write them all down explicitly. (Here, D6 is the dihedral group of order 12, i.e. it is the group of symmetries of the regular hexagon.)
(b) Exhibit a proper subgroup of D6 which is not cyclic.
Homework Equations
The Attempt at a Solution
so far i know that..
D6 = {I, R1, R2, R3, R4, R5, S1, S2, S3, S4, S5, S6} where, I is the identity, R1-R5 are rotations (60, 120, 180, 240, 300 degrees respectively) and S1-S6 are the 6 reflections across the 6 different reflective axes of the hexagon.
I'm not sure where to go from here, any help at all would be greatly appreciated!
thanks!:)