Results 1 to 4 of 4

Math Help - This is an easy answer but i dont get it.

  1. #1
    Senior Member sfspitfire23's Avatar
    Joined
    Oct 2009
    Posts
    273

    This is an easy answer but i dont get it.

    OK, t_{ab}=ax+b. I have to prove this is a subgroup of S4. Now, Ive already proved closure by composition t_{ab}=ax+b with t_{cd}=cx+d to yield (ac)x+(ad+b).

    Now, the identities wrt composition are a=1 and b=0. What is the inverse!? How would you find the inverse wrt composition here?


    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by sfspitfire23 View Post
    OK, t_{ab}=ax+b. I have to prove this is a subgroup of S4. Now, Ive already proved closure by composition t_{ab}=ax+b with t_{cd}=cx+d to yield (ac)x+(ad+b).

    Now, the identities wrt composition are a=1 and b=0. What is the inverse!? How would you find the inverse wrt composition here?


    Thanks!
    A subroup of...who??

    Anyway, it must be that T_{\alpha \beta}T_{ab}=x \Longrightarrow (a\alpha)x+(a\beta +b)=x

    Well, now just solve the above for \alpha\,,\,\,\beta

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member sfspitfire23's Avatar
    Joined
    Oct 2009
    Posts
    273
    So there indeed will be 2 inverses?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by sfspitfire23 View Post
    So there indeed will be 2 inverses?

    Of course not: this is a group. What gave you that idea?

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 28th 2010, 08:31 AM
  2. Replies: 11
    Last Post: November 1st 2009, 09:12 AM
  3. Function question (easy but i dont understand)
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: January 30th 2009, 09:00 PM
  4. Replies: 2
    Last Post: July 4th 2008, 12:27 PM
  5. Replies: 1
    Last Post: October 25th 2006, 05:25 PM

Search Tags


/mathhelpforum @mathhelpforum