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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?

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# Intersections of Sylow p-groups

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