List down the elements of the following subgroups of Zp²q² <1>= = = = < 9² >= = = = =

Q: 8. Find a non-trivial normal subgroup of the octic group. Demonstrate that this subgroup is normal.

A: According to the given information, it is required to find a non-trivial normal subgroup of the…

Q: give the order of the element in the in the factor group (2,5) + in (Z3 x Z6)/

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Q: If H and K are subgroups of G, |H|- 16 and K-28 then a possible value of HNK| is 16

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Q: Find the line that best fit the data 2 [8] [8] [3]- "

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Q: Find the characteristic of Z4 ⨁ 4Z.

A: Given: ℤ4⊕4ℤTo find: The characteristic of ℤ4⊕4ℤ.

Q: Define :normal subgroup

A: To write the definition of normal subgroup

Q: Define Group theory ?

A: To define group theory

Q: Is {0, 2, 4, 6} a subgroup of Zg? Justify your answer.

A:

Q: 13. Which of the following is a subgroup of (R+, *) where a*b = (ab)/2? (Q, *) A. B. (Z, *) C. (Q+,…

A: Given that                    ℝ+, * is a group             where…

Q: Denote by X₁1 the operation "multiplication modulo 11" where a X11 b is the remainder when a × b is…

A: The given set Z11=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. To construct the multiplication modulo table,…

Q: Determine whether the intersection of normal subgroups is a normal subgroup. Show your work.

A: A subgroup H of a group G is normal normal in  G if and only if xHx−1⊆H   ∀x∈G.A nonempty subset H…

Q: Find the number of sylow 5 subgroups, sylow 7 subgroups and sylow 2 subgroups of A5

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Q: 12. Find all subgroups of Z2×Z4.

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Q: السؤال 17 2.5 نقطة )نقاط( For the group D3, the value of U2 µ3 is Po

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Q: Illustrate the Abel's Formula?

A: To  illustrate the Abel's Formula.

Q: Consider S4 and its subgroups H = {i,(12)(34),(13)(24),(14)(23)} and K = {i,(123),(132)}. For a =…

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Q: 4 (a) Find a Sylow 5-subgroup of Sg. How many such subgroups are there ? How many 5- cycles are…

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Q: what do the ks stand for in the exel tables

A: The Runge-Kutta method is a numerical technique used to solve ordinary differential equations (ODEs)…

Q: Determine the groups of order 45

A: By Sylow's theorems, the number of Sylow 3-subgroups must divide 45 and be congruent to 1 modulo 3,…

Q: Answer the followings: 1. Let p = (1 2 4 5) (36) € 56. Find the index of (p) in 56. a. 60 b. 120 C.…

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Q: How many elements does the group of rotations of a regular hexagon have?

A: The group of rotations of a regular hexagon is D6. And as the order of the group Dn is 2n.

Q: Write a Cayley table for the dihedral group D6 = {1, r,r^2,s,sr,sr^2|

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Q: Find all the cosets of the subgroup 4Z of Z

A: In the group of integers under addition, the subgroup consists of all multiples of 4, i.e., .A coset…

Q: what is the characteristic of Z6xZ9

A:

Q: 9. Find all proper nontrivial subgroups of Z₂ × 2₂.

A: The given group is: .To Do: We have to find all proper nontrivial subgroups of .Note: Since you have…

Q: Find four different subgroups of S4 that are isomorphic to S3.

A: If there exists an isomorphism between the subgroups they are called isomorphic ( Isomorphism is…

Q: X={1,2,0,,8,3,5}. (a) Find all possible permutations and show that its form a group. (b) Find its…

A: Note: According to our guidelines We’ll answer the first 3 subparts of the question since the exact…

Q: How many subgroups does (Z36) have? What are they?

A:

Q: 5. arcsin 1

A: Solution ) arcsin1 = sin-1(1) [ Sin (π/2) = 1 ] Sin-1(sin(π/2) ) =π /2 Or in radian = 1.5714

Q: 5.1 In each case, determine whether or not H is a subgroup of G. a) G=(R, +); H=Q b) G=(Q, +); H=Z…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

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 .

Q: 3. consider the group D4 = {(1), (1234), (13), (24), (1432), (12), (34), (14), (23), (13), (24)} a.…

A: To enumerate all the distinct subgroups of the group D₄, we need to consider all possible…