Results 1 to 2 of 2

Math Help - Showing H and Ha have same cardinality

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    66

    Post Showing H and Ha have same cardinality

    OK this was a question from a test ill post the question and then how i answered and i was hoping to get a "correct answer" and whether what i said was even close.

    Let H be a subgroup of G. Show directly that H and Ha have the same cardinality.

    I couldnt figure anything out proof wise so heres what i said:

    H is a subgroup of G so H is finite and has elements h1,h2,...,hn all of which are distinct. Ha is the set {x in G | x = ha h in H} then Ha takes elements in H and multiplies (perform operation) on the right by a, since all elements in h are distinct then all h1a,h2a,...hna will be distinct so they must be the same size

    I couldnt figure out a proof so i was trying to reason through it
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by ChrisBickle View Post
    OK this was a question from a test ill post the question and then how i answered and i was hoping to get a "correct answer" and whether what i said was even close.

    Let H be a subgroup of G. Show directly that H and Ha have the same cardinality.

    I couldnt figure anything out proof wise so heres what i said:

    H is a subgroup of G so H is finite and has elements h1,h2,...,hn all of which are distinct. Ha is the set {x in G | x = ha h in H} then Ha takes elements in H and multiplies (perform operation) on the right by a, since all elements in h are distinct then all h1a,h2a,...hna will be distinct so they must be the same size

    I couldnt figure out a proof so i was trying to reason through it

    The map h\mapsto ha is an obvious bijection between H\,\,\,and\,\,\,Ha

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cardinality
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: December 7th 2010, 10:01 AM
  2. Replies: 1
    Last Post: September 27th 2010, 11:06 PM
  3. Cardinality
    Posted in the Discrete Math Forum
    Replies: 15
    Last Post: April 5th 2010, 02:16 PM
  4. Cardinality of a Set
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: January 27th 2009, 03:33 PM
  5. cardinality
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 15th 2008, 07:18 PM

Search Tags


/mathhelpforum @mathhelpforum