Results 1 to 2 of 2

Math Help - grouop of order 4

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    42

    grouop of order 4

    1. Let G be a group of order 4. Prove that every element of G has order 1,2, or 4.

    2. Classify groups of order 4 by considering the following two cases:
    a. G contains an element of order 4
    b. Every element of G has order <4


    could anyone please help me to solve these problems?
    and what does it mean by 'Classify groups of order 4'?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    ynj
    ynj is offline
    Senior Member
    Joined
    Jul 2009
    Posts
    254
    the group itself will have order 4,|e|=1
    for any element a, |a|=1 or 2 or 4
    if |a|=1 then a=e
    if there is an a such that |a|=4, than it would be a cyclic, thus isomorphic to Z(4), so it will also have subgroup of order 2.
    if such element does not exist, then 3 elements will have order 2, that is, isomorphic to Z(2)*Z(2).
    "classify"actually means classify the group up to isomorphism
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Re-writing higher order spatial derivatives as lower order system
    Posted in the Differential Equations Forum
    Replies: 11
    Last Post: July 27th 2010, 09:56 AM
  2. Replies: 1
    Last Post: October 27th 2009, 05:03 AM
  3. Replies: 2
    Last Post: February 23rd 2009, 06:54 AM
  4. Replies: 2
    Last Post: January 9th 2009, 08:31 PM
  5. Replies: 2
    Last Post: November 25th 2008, 10:29 PM

Search Tags


/mathhelpforum @mathhelpforum