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Intersection of Groups

  1. Sep 24, 2008 #1
    1. The problem statement, all variables and given/known data
    If H, K are subgroups of G, show that H intersect K is a subgroup of H

    2. Relevant equations
    I know that H intersect K is a subgroup of G; I proved this already but I'm wondering how H intersect K is a subgroup of H

    3. The attempt at a solution
    I'm quite sure this is true but my idea is based on set theoretic properties and one can't use such properties to apply on subgroups
  2. jcsd
  3. Sep 24, 2008 #2


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    If you've proved H intersect K is a group, then there is nothing more to prove. H intersect K is contained H and it's a group. Therefore it's a subgroup of H. That's the definition of 'subgroup'.
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