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Ad Infinitum NAU

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Anyhow, I'll get to my discussion..

I'm graduating in May with my BS in Math/Physics. I'm currently doing independent studies in Coding Theory as well as some higher abstract algebra.

I've been working on a problem I found in an old Abstract Algebra book for 3.5 weeks now and I finally have it solved but my details aren't clear enough for my satisfaction.

The detail I'm trying to pretty-up is: I've got three 2-Sylow subgroups of a group G where |G| = 48, and so the orders of the Hi's are 16 (where the Hi's are the 2-Sylow subgroups. I would like to show that |H1 intersect H2| = |H1 intersect H3| = |H2 intersect H3|

any idears?