# Group and subgroup example

1. Jan 30, 2012

### blahblah8724

In an example it says that, if $|G| = 15$ and $G$ has subgroups $A,B$ of $G$ with $|A| = 5$ and $|B| = 3$, then $A \cap B$ must equal $\{e_G\}$ and the smallest subgroup of $G$ containing both $A$ and $B$ is $G$ itself. Could anyone explain why? Thanks!

2. Jan 30, 2012

### morphism

Hint: Lagrange