Results 1 to 3 of 3

Math Help - sub-groups

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    7

    sub-groups

    Is G a finite group , H , K subgroups such that H K.
    Prove [ G:H ] = [ G:K ] . [ K:H ]

    Please can develop it in detail.

    THANKS YOU FRIENDS....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Its just a simple application of Lagrange:

    [G:H]=\frac{ \vert G \vert }{ \vert H \vert } and \vert H \vert = \frac{ \vert K \vert }{ [K:H] } substitute in the first and you get [G:H] = \frac{ \vert G \vert }{ \vert K \vert } [K:H] = [G:K][K:H]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    7

    help

    thanks for the help, that I needed to think a bit
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. About minimal normal groups and subnormal groups
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: October 20th 2011, 02:53 PM
  2. Automorphism groups of cyclic groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: August 15th 2011, 10:46 AM
  3. Quotient Groups - Infinite Groups, finite orders
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: August 11th 2010, 08:07 AM
  4. free groups, finitely generated groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 23rd 2009, 04:31 AM
  5. Order of groups involving conjugates and abelian groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: February 5th 2009, 09:55 PM

Search Tags


/mathhelpforum @mathhelpforum