Show that {t_(1,s) : 2 ≤ s ≤ n} is a minimal generating set for S_n....

Show that {t_(1,s) : 2 ≤ s ≤ n} is a minimal generating set for S_n. You may use the fact that {t_(r,s) : 1 ≤ r < s ≤ n}, as defined in the outline, generates S_n.

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Expert Solution

It is required to show that the (n-1) transpositions as above is a minimal generating set for Sn. The proof submitted involves 3 parts. First it is proven that transpositions generate Sn. Then it is proven that the given (n-1) transpositions generate Sn. Finally it is shown that the given (n-1) transpositions is a minimal generating set for Sn.

Colby Messinger answered 1 year ago

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