Results 1 to 4 of 4

Math Help - findng a group between two groups...

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    1

    findng a group between two groups...

    we all know that set of rationals is a subgroup of set of reals under the group law multiplication. my question is whether there exsts a group between these tw groups. f yes what it can be? and if no, how to prve the non-existence?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by anugrah View Post
    we all know that set of rationals is a subgroup of set of reals under the group law multiplication. my question is whether there exsts a group between these tw groups. f yes what it can be? and if no, how to prve the non-existence?
    Algebraics?

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member JaneBennet's Avatar
    Joined
    Dec 2007
    Posts
    293
    Quote Originally Posted by anugrah View Post
    we all know that set of rationals is a subgroup of set of reals under the group law multiplication. my question is whether there exsts a group between these tw groups. f yes what it can be? and if no, how to prve the non-existence?
    Do you mean set of nonzero rationals and set of nonzero reals under multiplication? If d is any square-free positive integer (i.e. not a perfect square), the set A of all a+bd, where a and b are rationals and not both 0, is a multiplicative group lying strictly between the multiplicative groups of the nonzero rationals and the nonzero reals.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    There are many such groups.
    Let \alpha = \sqrt[n]{p} for a prime p.
    Then let \mathbb{Q}( \alpha) = {a_0+a_1\alpha+...+a_{n-1}\alpha^{p-1} } where a_0,a_1,...,a_{n-1} are in Q.
    Then this is a group under addition and multiplication (without zero).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Given a group how to investigate groups that are homomorphic to it
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: May 14th 2011, 05:29 PM
  2. Cyclic Groups - Is it a Cyclyc group?
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: August 12th 2010, 04:10 AM
  3. Factor groups for the quaternion group?
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 9th 2009, 02:29 AM
  4. Groups- Proof using on the defination of a group
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: October 6th 2009, 03:08 PM
  5. Groups - Alternating group question
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: May 9th 2009, 12:35 AM

Search Tags


/mathhelpforum @mathhelpforum