# Sylow subgroups and their intersections.

I have just read in some online lecture notes that:

Since $b$ is a prime, any two distinct Sylow $b$-subgroups have intersection $\{id\}$.

Can anyone explain why this is true? I'm new to Sylow theory, so apologies if it's a very easy question.

• Please note that taking sentences out of context can be confusing or misleading. This is to be avoided here, since people willing to answer may be put off by a statement that is visibly incomplete.. In this case, my bet would be that the order of the group in question is divisible by the prime $b$, but not by $b^2$, so the order of a $b$-Sylow subgroup is $b$. Then the statement follows from Lagrange's theorem. – Andreas Caranti Feb 4 '17 at 14:25