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Multiply Transitive Groups

  1. Dec 29, 2012 #1
    Hi All,

    I have a hard time answering the following. I need some help.

    Let Z={a,b,c,d,e,f} and let X denote the set of 10 partitions of Z into two sets of three. Label the members of X as follows:

    0 abc|def
    1 abd|cef
    2 abe|cdf
    3 abf|cde
    4 acd|bef
    5 ace|bdf
    6 acf|bde
    7 ade|bcf
    8 adf|bce
    9 aef|bcd

    Let g->g^ denote the representation of S6=Sym(Z) as permutations of X.

    1. By considering (abc)^ and (def)^, show that (S6)^ is 2-transitive on X.

    2. How many elements of (S6)^ fix both 0 and 1? Find them. Deduce that (S6)^ is not 3-transitive on X.

    Thank you very much. :)
  2. jcsd
  3. Dec 30, 2012 #2
    I have already solved the problem.thank you.
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