0
$\begingroup$

I need a counterexample to the following statement: if A, B are subgroups of a group G, and A is a normal subgroup of B, B is a normal subgroup of G, then A is a normal subgroup of G. I've tried using groups such as $Z/nZ$ and $Z_n^{*}$, but neither seem to work. Thanks for your help.

$\endgroup$
2

1 Answer 1

0
$\begingroup$

Consider $A_4$. We have $\Bbb{Z}_2 \unlhd V_4 \unlhd A_4$ but $\Bbb{Z}_2$ is non-normal in $A_4$

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.