Why should the intersection of two normal subgroups be trivial.

Question

Why intersection of two normal subgroups is trivial ?

I know this is simple but I cant get it. $|G|=11^{2}13^{2}$

$H$ and $K$ are $11$ and $13$ Sylow normal subgroups respectively .
Then why must be $H\cap K=e$ ? I am stuck on it for an hour or so.

score 2 · Accepted Answer · answered May 07 '16 at 11:13

2

HINT

Every element of $H$ have order dividing $11$ and every element of $K$ have order dividing $13$.

$H \cap K$ is a subgroup of both. What can you say about the order of elements of subgroups?

answered May 07 '16 at 11:13

Fredrik Meyer

I knew that it should be simple.Thank you very much for ending my agony. – kadir May 07 '16 at 11:21

1 Answers1