1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Findng a group between two groups

  1. Jul 24, 2008 #1
    we all know that set of rationals i a subgroup of set of reals. 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?
     
  2. jcsd
  3. Jul 24, 2008 #2
    There exist uncountably many. (We assume that you mean addition as the group law.)
     
  4. Jul 24, 2008 #3

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    It will help your intuition if you notice that the reals form a 'very large' vector space over the rationals.
     
  5. Jul 24, 2008 #4
    sorry, forgot to mention that the group law is multiplication. I wanted everything with respect to multiplication. And if there exists a subgroup between these two groups (even with respect to addition ) please give an example of the same.
     
  6. Jul 24, 2008 #5
    Pick any irrational number k and consider the set Q'={qkn | q is a nonzero rational number, and n is an integer}

    It is easy to show that this is a group under multiplication, and easy to show that the nonzero rationals are a subgroup of this group, but clearly since this group is countable it is proper subgroup of the reals.
     
  7. Jul 25, 2008 #6
    The real numbers under multiplication are not a group.


    It would be better if you tried to work it out yourself.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Findng a group between two groups
Loading...