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Multiply Transitive Groups 
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#1
Dec2912, 08:06 AM

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 abcdef 1 abdcef 2 abecdf 3 abfcde 4 acdbef 5 acebdf 6 acfbde 7 adebcf 8 adfbce 9 aefbcd Let g>g^ denote the representation of S6=Sym(Z) as permutations of X. 1. By considering (abc)^ and (def)^, show that (S6)^ is 2transitive on X. 2. How many elements of (S6)^ fix both 0 and 1? Find them. Deduce that (S6)^ is not 3transitive on X. Thank you very much. :) 


#2
Dec3012, 01:31 PM

P: 3

I have already solved the problem.thank you.



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