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Group Theory

  1. Nov 14, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the three 2-Sylow subgroups of ##S_3## and find a 2-Sylow subgroup and a 3-Sylow subgroup of ##S_4.##

    2. The attempt at a solution

    I got ##|S_3| = 6 = 2\dot\ 3## and ##|S_4| = 24 = 2^3\dot\ 3.## So ##S_3## has a a Sylow 2 subgroup of order 2 and a Sylow 3 subgroup of order 3. I am asked to find the three 2-Sylow subgroups of ##S_3## so since the 2-Sylow of ##S_3## has order 2 is it just the permutations ##(1 2), (1 3), (2 3)? ##
     
  2. jcsd
  3. Nov 14, 2013 #2

    pasmith

    User Avatar
    Homework Helper

    Those are the generators of the only subgroups of [itex]S_3[/itex] of order 2, so yes.
     
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