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Group Theory Help

Let G be the dihedral group 12

Is this correct: H=<r^3,s> = { e, r^2, r^3, s, r^3s }?

Tha answer has { e, r^3, s, r^3s }

Thank you.
Original post by e^x
Let G be the dihedral group 12

Is this correct: H=<r^3,s> = { e, r^2, r^3, s, r^3s }?

Tha answer has { e, r^3, s, r^3s }

Thank you.


Bit rusty. I presume this is D6D_6 with 12 elements, r being a rotation through pi/3, and s a reflection (of some description).

And H is the subgroup generated by the two elements r3,sr^3,s

Where does your r2r^2 come from?
Reply 2
Original post by ghostwalker
Bit rusty. I presume this is D6D_6 with 12 elements, r being a rotation through pi/3, and s a reflection (of some description).

And H is the subgroup generated by the two elements r3,sr^3,s

Where does your r2r^2 come from?


s is a reflection in the vertical axis.

I got r^2 when I square r^3 to get r^6 which is the same as r^2?
Reply 3
Original post by ghostwalker
Bit rusty. I presume this is D6D_6 with 12 elements, r being a rotation through pi/3, and s a reflection (of some description).

And H is the subgroup generated by the two elements r3,sr^3,s

Where does your r2r^2 come from?


I've just realised that I was taking r as a rotation by pi/4 instead of pi/3. I'll take a look my working out in the morning and post again if I need help.

Thanks.
Original post by e^x
s is a reflection in the vertical axis.

I got r^2 when I square r^3 to get r^6 which is the same as r^2?


r^6 = e

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