Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Quick question about Lagrange's theorem

  1. Sep 22, 2016 #1

    TeethWhitener

    User Avatar
    Science Advisor
    Gold Member

    I was looking at the proof of Lagrange's theorem (that the order of a group ##G## is a multiple of the order of any given subgroup ##H##) in Wikipedia:



    I understand this proof fine, but I was wondering, instead of finding a bijection between cosets, is it enough to find a bijection between an arbitrary coset ##gH## and the subgroup ##H##? So, for instance, we have a map ##f: gH \rightarrow H##, where ##f(x) = g^{-1}x##. The map is bijective, with inverse ##f^{-1}(y) = gy##. Is there anything wrong with this?
     
  2. jcsd
  3. Sep 22, 2016 #2

    fresh_42

    Staff: Mentor

    No. Whether you show ##|aH|=|bH|## for arbitrary ##a\, , \, b## or ##|aH|=|H|=|eH|## for all ##a## doesn't make a difference. And ##"="## is transitive. It's simply a matter of taste.
     
  4. Sep 22, 2016 #3

    TeethWhitener

    User Avatar
    Science Advisor
    Gold Member

    Cool, thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Quick question about Lagrange's theorem
  1. Quick question about Pi (Replies: 13)

Loading...