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.
Sylow subgroups and their intersections.
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group-theory
sylow-theory
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1Please 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. – 2017-02-04