# Math Help - subgroup and orders, H∩K={e}

1. ## subgroup and orders, H∩K={e}

Suppose H and K are distinct subgroups of a finite group G, and the orders of H and K are relatively prime, then prove H∩K={e}

2. Pick $a \in H \cap K$ then if $ord(a)=b$ we have $b \vert \vert H \vert$ and $b \vert \vert K \vert$ so $b \vert (\vert H \vert , \vert K \vert )=1$ so...