- #1

Daniiel

- 123

- 0

I've been trying to solve this question,

Show that <a in D8 : a

^{2}=1> is a not a group.

I might not be processing it properly, but my interpretation of the question is that

<a in D8 : a

^{2}=1> = <(a,b): a

^{2}=e, b

^{2}=2, ab=a

^{-1}b>

Which is just D4, a group, the set of dihedral where 2n=4,

Is the proper interpretation supposed to be

<a in D8 : a

^{2}=1> = <(a,b): a

^{2}=e, a

^{4}=e,b

^{2}=2, ab=a

^{-1}b>

which is again D4,

Could anyone help me interoperate the question