Subgroup of D_n: Proving <f> Not Normal

[rapple]

Homework Statement

S.T <f> is not normal. where f is a reflection

Homework Equations

<f>={e,r^0 f, r^1f,r^2f,..}
WTS For any g in D-n, g(r^kf)g^-1 Not In <F>

The Attempt at a Solution

Elements of D-n are r^k, r^kf
For r^k, (r^k)(r^if)(r^-k) is in <f>.

So I am stuck

 

[Billy Bob]

WTS For any g in D-n, g(r^kf)g^-1 Not In <F>

No. You want to show there exists such a g. Just find one.

 

[matt grime]

The subgroup generated by f, which is what <f> usually means, is just {e,f} with e the identity. What you wrote is in fact all of D_n. You probably should write in proper sentences so that everyone is sure what you mean (i.e. no abbreviations that might not be universally understood) - reading mathematics is hard at the best of times, so please help us out and make it as easy as possible.