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Group with subgroups proof

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Let G be a group with subgroups H and K. Prove HintersectK is a subgroup.

    2. Relevant equations



    3. The attempt at a solution
    G is a group with subgroups H and K. Then H and K are closed, have identity elements in G and have inverses.
    HintersectK is a subgroup because H and K must satisfy the same properties of G.
     
  2. jcsd
  3. Mar 30, 2009 #2
    let [tex] a,b \epsilon H [/tex] and [tex] a,b \epsilon K [/tex].Then [tex] a*b \epsilon H [/tex] and [tex] a*b \epsilon K [/tex].Let [tex] a \epsilon H [/tex] and [tex] a \epsilon K [/tex].Then [tex] a^{-1} \epsilon H [/tex] and [tex] a^{-1} \epsilon K [/tex].
     
  4. Mar 30, 2009 #3
    that makes sense
     
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