Show that Sn = <(1, 2), (1, 2 , ..., n)>
Show that Sn = <(1, 2), (1, 2 , ..., n)>
suppose n greater than or equal to 2. Prove that Sn
is generated by each of...
suppose n greater than or equal to 2. Prove that Sn
is generated by each of the following sets
a) T1= { (1,2) , (1,2,3, .. , n)}
b) T1= { (1,2,3,... , n-1), (n-1,n)}
c) T1= { (1,2), (2,3),(3,4), ... , (n-1,n)}
c) T1= { (1,n), (2,n),(3,n), ... , (n-1,n)}
If kr<=n, where 1<r<=n. Prove that the number of
permutations α ϵ Sn, where α is...
If kr<=n, where 1<r<=n. Prove that the number of
permutations α ϵ Sn, where α is a product of k disjoint r-cycles is
(1/k!)(1/r^k)[n(n-1)(n-2)...(n-kr+1)]