1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lagranges Theorem

  1. May 22, 2008 #1
    The definition I have is:

    Leg G be a finite group and let H be a subgroup of G. Then the order of H is a factor of the order of G. More precisely, |G|=m|H| where m is the number of different cosets of H in G.

    Can someone clarify what the | | means?

    I thought it was how many elements are in a group, such as, the symmetric group of 4 (S4) has 4! elements, so |S4| = 24.

    I have an example saying the S4 cannot have a subgroup of order 5 since |S4| = 24 which is not an exact multiple of 5.

    But 24 is the number of elements in S4, not the order of the group.. So why are they saying the subgroup can't have order 5 because of the number of elements in S4? Surely we should be finding the order of S4 instead to se if there is a subgroup of order 5 in the group.

  2. jcsd
  3. May 22, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    The order of a group G is the number of elements in the group G, which is denoted as |G|. I don't know what is confusing you.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Lagranges Theorem
  1. Lagrange's Theorem (Replies: 1)