Let G = U(15) and H ={1,14} be a subgroup of G. The distinct left cosets of H in G are: * None of the choices {Н, 2H, 7H, 14Н)} (Н, 2H, 4H, 13н} {H, 2H, 8H, 11H}

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A: Given that 2Z is the set of all even integers.

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Q: 2. If a is an involution, then Baß is an involution for any transformation B.

A: It is given that α is an involution. So, we can say that α2=I.

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Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -3 + 2Z contains the…

A: Given: 2Z is a subgroup of (Z,+). We have to find the right coset of -3+2Z.

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A: It is given that x and y be two vertices of a Cayley digraph. We can write two paths as a1,a2,a3,…an…

Q: 5. Let H= [ (û ¿)I a,b,c EIRI, show that: (H,+) is a sub gromp of (M,+).

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Q: Question 3: a. Let (H,+) ≤ (R, +), let K = {2h : h E H}. Prove that (K,x) ≤ (R*,x). (Clarification:…

A: We shall use subgroup test to solve this problem

Q: is a subgroup of Z, of order 12 O 12 5, 3.

A: The explanation of the solution as follows:

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A: We have to solve given problem:

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A: Given G=U(18)  H ={1,17} We need to find the number of distinct left cosets of H in G

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Q: Find the partition of Ze into cosets of the subgroup H = {0,3}.

A: In this problem we have to find the partition of  into cosets of the subgroup .