Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By johng

Math Help - 2 similar questions dealing with symmetric groups, Sylow, finding index and order...

  1. #1
    Junior Member
    Joined
    Apr 2013
    From
    Canada
    Posts
    42
    Thanks
    2

    2 similar questions dealing with symmetric groups, Sylow, finding index and order...

    "If G is a subgroup of the symmetric group S_n which contains an odd permutation, then G is a subgroup of index 2"

    "If G is a group of order (2^k)m, m odd, and the Sylow 2-subgroups of G are cyclic, then G has a normal subgroup of order m. Hint: Let G act on G by left multiplication and apply the preceding problem."

    I posted these questions together since they seem to be very similar.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    547
    Thanks
    220

    Re: 2 similar questions dealing with symmetric groups, Sylow, finding index and order

    Here's a solution:

    2 similar questions dealing with symmetric groups, Sylow, finding index and order...-mhfgroups5.png
    Thanks from HowDoIMath
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding element of maximal order in symmetric group
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 13th 2009, 10:20 PM
  2. Finding all groups of order n up to isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 8th 2009, 02:55 AM
  3. A Couple Questions Dealing With Finite Groups
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 22nd 2009, 08:48 PM
  4. Symmetric Groups Questions
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 22nd 2009, 01:00 PM
  5. Group Theory: finding groups of order 160
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 24th 2008, 05:54 PM

Search Tags


/mathhelpforum @mathhelpforum