hello everyone. Can any one help me on this:
H and K are subgroups of G, K is also normal in G.
I want to find a counterexample that HK is not normal in G.
Thanks!!
Hi NonCommAlg.
As xxie didn’t state any condition on what type of normal subgroup $\displaystyle K$ should be, my example was a fair one.
But, if you like, how about
$\displaystyle G=D_6=\left<\rho,\sigma:\rho^6=\sigma^2=1,\, \rho\sigma=\sigma\rho^{-1}\right>$
$\displaystyle H=\{1,\sigma\}$
$\displaystyle K=\{1,\rho^3\}=Z\left(D_6\right)$