Results 1 to 2 of 2

Math Help - Isomorphism from C^* to G/H

  1. #1
    Senior Member
    Joined
    Dec 2008
    Posts
    288

    Isomorphism from C^* to G/H

    If we have the group G=(C^*,\times) and the subgroup H=\{\pm1,\pm i\}. Prove that (C^*,\times)/H is isomorphic to (C^*,\times).

    Im confused about this a bit.

    As the cosets of H in G are \{\pm a\pm ib\}\ \forall{a,b}\in\mathbb{R}.

    Surely they are not isomorphic?

    Thanks for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Feb 2008
    Posts
    410

    Re: Isomorphism from C^* to G/H

    Define \varphi:\mathbb{C}^\times\to\mathbb{C}^\times by \varphi(z)=z^4. Prove that \varphi is a group homomorphism and apply the first isomorphism theorem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: October 27th 2010, 12:08 AM
  2. isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 30th 2010, 09:52 AM
  3. isomorphism
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 10th 2010, 08:50 AM
  4. Replies: 4
    Last Post: February 14th 2010, 03:05 AM
  5. Isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: June 28th 2009, 11:13 PM

Search Tags


/mathhelpforum @mathhelpforum