Results 1 to 2 of 2

Math Help - group theory

  1. #1
    Junior Member
    Joined
    Oct 2006
    Posts
    33

    group theory

    can someone help me with this questuon please its fundamnetal to the topic and preventing me understand the topic!!

    Thanks

    Edgar

    if G is a group and n > or equal to 1 define

    G(n) = {x element of G : ord (x) = n}

    If G is isomorphic to H show that for all n greater than or equal to 1
    mod G(n) = mod H(n)

    Deduce that C(subscript 3) * C(subscript 3) is not isomorphic to C(subscript 9)

    Is it tru that C 3 * C 5 is isomorphic to C15

    whats going on here!!?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    What does this have to do with linear algebra?
    Quote Originally Posted by edgar davids View Post
    can someone help me with this questuon please its fundamnetal to the topic and preventing me understand the topic!!

    Thanks

    Edgar

    if G is a group and n > or equal to 1 define

    G(n) = {x element of G : ord (x) = n}

    If G is isomorphic to H show that for all n greater than or equal to 1
    mod G(n) = mod H(n)
    Mod, what? n? (Again finite I think)
    Since they are isomorphic they certainly have the same number of elements.
    Thus, |G(n)|=|H(n)|, then certainly a weaker statement |G(n)|\equiv |H(n)|(\mbox{ mod }n)
    Deduce that C(subscript 3) * C(subscript 3) is not isomorphic to C(subscript 9)

    Is it tru that C 3 * C 5 is isomorphic to C15

    whats going on here!!?
    What is C? The cyclic group?

    You can just use the fundamental theorem,
    C_3 \times C_3 \not \simeq C_9
    Because they are distinct prime power decompositions.

    C_3\times C_5 \simeq C_{15}
    Because \gcd(3,5)=1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 4th 2009, 09:52 AM
  2. Quick questions on Group Theory - Cosets / Normal Group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 16th 2009, 08:39 AM
  3. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 11:10 AM
  4. Group Theory Question, Dihedral Group
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 4th 2008, 10:36 AM
  5. Group Theory
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 12th 2007, 09:28 AM

Search Tags


/mathhelpforum @mathhelpforum