# Multiply Transitive Groups

by laptopmarch
Tags: permutation group, transitive
 P: 3 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. :)
 P: 3 I have already solved the problem.thank you.

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