Given n N with n 2 , let T S n be the subset consisting of the permutations that leave 1 fixed T S n ( 1 ) 1 (a)Show that T is a subgroup of S n (b)Show that T S n 1 Given EN with 2, let I C S be the subset consisting of the permutations that leave 1 fixed I fo ES 0 ( 1 ) 17 ( a ) Show that I is a subgroup of S ( b ) Show that I S 1

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Question: Given n N with n 2 , let T S n be the subset consisting of the permutations that leave 1 fixed: T :={S n

Given n Nwithn 2,letT S_nbe the subset consistingofthe permutations that leave1fixed: T :={S_n | (1)=1}.

(a)Show that T is a subgroup of S_n.
(b)Show that T S_n-1.

Given ~ EN with ~ > 2, let I C S be the subset consisting of the permutations that leave 1 fixed : I : _ fo ES~ |0 ( 1 ) = 17. ( a ) Show that I is a subgroup of S . ( b ) Show that I ~ S- - 1

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