Find normalizer and centralizer of the subset H = {1, r2 , r2 s} of the group D5= The dihedral group of order 10.

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A: For G/H : H=0,9,18,271+H ={1,10,19,28}..........8+H={8,17,26,35} For G/K:…

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Q: Q3:(A) Prove that every group of order 15 is decomposable and normal. (B) Show that (H,.) is a…

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Q: In Z₁6, write down all the cosets of the subgroup H = {[0], [4], [8], [12]}. (Since the operation in…

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Q: 2. Let G = Z50 and consider it's subgroup H = (5). Find all coset representatives of 3+ H.

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Q: Q3:(A) Prove that every group of order 15 is decomposable and normal. (B) Show that (H,.) is a…

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Q: Enter the smallest subgroup of M₂ (R)* containing the matrix -5 -3 7 4 as a set

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Q: In the group U (16) compute, (a) 5-7, and (b) 3-1

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Q: prove or disprove The intersection of any two distinct left cosets in the group is empty set

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Q: In the group U (I6) compute, (a) 5.7, and (b) 3

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Q: (a) (N,), a 2. (b) (C\{0},), a = i. (c) (Z2×2,), a = [7]. (d) (R³, +), a = (1, −1, 1, −1, 1, . . .).…

A: (a) Here .Noted that there is no positive integer  .Hence no finite order exists for  .also there is…