SOLUTION: In permutation group 𝑆6, if 𝛼 = (2 3 4) and 𝛽 = (2 5 6), then find a permutation 𝜙 such that 𝜙𝛼𝜙 −1 = 𝛽. Let 𝑎 be a fixed element of a ring R, and

Question 1182331: In permutation group 𝑆6, if 𝛼 = (2 3 4) and 𝛽 = (2 5 6), then find a permutation 𝜙 such that
𝜙𝛼𝜙
−1 = 𝛽.
Let 𝑎 be a fixed element of a ring R, and let
𝐼𝑠 = {𝑥 ∈ 𝑅 ∶ 𝑠𝑥 = 0}.
Show that 𝐼𝑠
is a subring of 𝑅.
Show that ℤ8 = {0,1,2,3,4,5,6,7,8} is a commutative ring w.r.t. addition modulo 8 and
multiplication modulo 8.
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
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