Results 1 to 2 of 2

Math Help - Prove a group

  1. #1
    Junior Member
    Joined
    Nov 2008
    Posts
    37

    Prove a group

    Prove that real number pairs  (a, b), where  a\neq 0, with operation \circ  form a group.
     (a, b) \circ (c,d)=(ac, ad + b).

    With what kind of mathematical concept and operation this group coincide?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Gamma's Avatar
    Joined
    Dec 2008
    From
    Iowa City, IA
    Posts
    517

    Group

    You must show it is closed under the operation, has an identity, is closed under inverses, and is associative.

    Closure is clear as + and * are closed in the reals, and R is a field, so it has no zero divisors. That is if a and c are not zero, their product is not zero.

    (a,b)\circ (1,0)= (a,b) so it has an identity.

    (a,b) \circ (1/a, -b/a)= (a/a, \frac{-ba}{a} + b)= (1,0)
    so it has inverses.

    I trust you can check associativity.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove group homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 29th 2010, 10:02 AM
  2. Prove Abelian group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 12th 2010, 09:52 PM
  3. Prove the LCM of an element in a group
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 18th 2010, 12:35 PM
  4. Prove S is a Group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 9th 2009, 05:56 AM
  5. Prove that in a group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 2nd 2008, 01:31 PM

Search Tags


/mathhelpforum @mathhelpforum