1. Not finding help here? Sign up for a free 30min 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!

Abstract Algebra - Subgroup of Permutations

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data
    A is a subset of R and G is a set of permutations of A. Show that G is a subgroup of S_A (the group of all permutations of A). Write the table of G.


    Onto the actual problem:
    A is the set of all nonzero real numbers.
    [itex]G={e,f,g,h}[/itex]
    where e is the identity element, f(x) = 1/x, g(x) = -x, h(x) = -1/x

    Would this be the right way to do it?

    For each combination of elements in G (call the elements a,b) I need to show
    a*b is in G

    I also need to show that the inverse of a is in G.

    Here is where I get confused, I'll start with with a = e:

    ee = e
    ef = f
    eg = g
    eh = h

    Okay, that is all good, now letting a = f:
    fe = e
    ff = e
    fg = h
    fh = g

    now a = g:
    ge = g !
    gf = h
    gg = g !
    gh = e

    now a = h:
    he = h
    hf = g !
    hg = f
    hh = g !

    What am I doing wrong here?
     
  2. jcsd
  3. Sep 28, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    The following are wrong:

    fe=e
    gg=g
    gh=e
    hg=f
    hh=g

    What did you do to obtain those?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Abstract Algebra - Subgroup of Permutations
Loading...