I want to understand this(adsbygoogle = window.adsbygoogle || []).push({});

If there exists more than one Sylow-p-subgroup of order p then for all these subgrps, their intersection is {e} the identity.

However if If there exists more than one Sylow-p-subgroup of order p^{k}s.t. k>0, then their intersection is not necessarily the identity element.

Is this correct? Can someone provide a quick explanation and proof please?

Does it have to do with homomorphisms to permutation groups?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Intersections of Sylow p-groups

**Physics Forums | Science Articles, Homework Help, Discussion**