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Counting Formula Clarification (Groups/Cosets)

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data


    G is a group. H is a subgroup.
    lHl= order of H
    lGl=order of G
    [G:H]=Number of cosets

    Counting Formula
    lGl = lHl [G:H]


    I have a question of clarification about this formula. My book says that [G:H]=number of cosets.

    The problem is that at this point in my book they haven't defined right cosests yet so I wasn't sure if
    [G:H]= The sum of the rights cosests and left cosets?

    or

    [G:H]= Just the left cosets?


    Thank you.
     
  2. jcsd
  3. Oct 19, 2011 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Just the number of left cosets which is equal to the number of right cosets.
     
  4. Oct 19, 2011 #3
    Thank you, HallsofIvy.
     
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