Recent content by chycachrrycol

  1. C

    Solved: Prove |HK|=|H||K| When H, K are Subgroups of G and H\capK = <e>

    So the problem is if H and K are subgroups of G with HK = {hk \in G| h \in H, k \in K}. If we know that H\capK = <e>, show |HK|= |H||K| My work so far: h, j \in H k,l \in K i know that if hk = jl then j^{-1}h = lk^{-1} But I'm not sure what to do from here.
  2. C

    Show one ring not isomorphic to the other

    How would we show that R X R X R X R is not isomorphic to M(R) with R being the set of real numbers. And more generally, what does it mean for one ring not to be isomorphic to another
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