How many subgroups are there in D4? Also find them.

Q: How many non-trivial subgroups in S3? 3 4 5

A: Trivial subgroup: A subgroup containing identity element is called as trivial subgroup and other…

Q: Write ?(16) as an internal direct product of its subgroups.

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Q: Sylow-5 subgroups-

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Q: Find the order of the group and the order of each element in the group. In each case, how are the…

A: In the given question we have to find the order of the group U(12) under multiplication modulo 12.…

Q: Build the operation table ∗ on G = {e, a, b} knowing that (G, ∗) is a group.

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Q: Q/ How many non-trivial subgroups in s, ? a) 2 b) 3 c) 4

A: S3 is the set of permutations on the set {1, 2, 3}S3={e, (1 2), (1 3), (2 3), (1 2 3), (1 3 2) }The…

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 cyclic subgroups of S4 that have three different orders.

A: There are more subgroups than just the cyclic ones.   Trivial:  there is <e> = {e}.   There…

Q: take the groups Z4 and Z5, what will be the elements of Z4 x Z5?

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Q: Find all the normal subgroups of D4.

A: To find all the normal subgroups of D4 .

Q: The number of subgroups of the group Z/36Z O 7 9 8. None of the choices 6.

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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: How many elements of a cyclic group with order 10 have order dividing 5?

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Q: How many non-trivial subgroups in S3? 3 4 2.

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Q: List all subgroups of Z15

A: We have to list all subgroups of Z15. Note that, Z15 is a cyclic group of order 15 and the set of…

Q: Find all subgroups of U(7)

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Q: Find subgroap order show a 4° and and are That normal sub graeps these in

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Q: How many non-trivial subgroups in S3? O 2 O 4 5 3.

A: To find the number of non trivial subgroups of S3.

Q: how that in D4 is not a normal subgroup. Please explain in details and show all the works.

A: To Show, a subgroup in D4 is not normal.

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: How many elements of order 33 are there in the dihedral group 33 ?D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: List all the subgroups of Z, including the “obvious" or “trivial" ones. Explain how you generated…

A: Group: A group is a set G together with a binary operation a, b↦a∗b:G×G→G satisfying the following…

Q: If H and K are subgroups of G, |H|= 18 and |K|=30 then a possible value of |HNK| is

A: It s given that H and K are subgroups of G, H=18 and K=30. Since H, K are subgroups, H∩K≤H  and…

Q: True or false? In the group (S3, ◦), (132)^−2 = (123).

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Q: Q/ How many non-trivial subgroups in s3 ? a) 2 b) 3 c) 4

A: We know that S3 = (1) , (1,2) , (1,3) , (2,3) , (1,2,3) , (1,2,3) Thus the subgroups of S3 are given…

Q: The elements of order 8 in the group (Zg ,+) is a)4 b) 5 c)6 d) 8

A: In this question we have to find the number of elements of order 8. (a) 4 is correct option

Q: How many subgroups of a

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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 * 4 O 16

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Q: How many Sylow 5-subgroups of S5 are there? Exhibit two.

A: We have that |Sn| = n! Hence, |S5| = 5! = 120 = 23.32.5 By Third Sylow Theorem the number of Sylow-5…

Q: How many non-trivial subgroups in S3? 4 O 5

A: Given group is S3 S3=3!=6 In total, there are 6 elements in the group S3 Elements of the given group…

Q: 50. How many proper subgroups are there in a cyclic group of order 12? A 4 в з с 2

A: see 2nd step

Q: How many cyclic subgroups does have U(15) have? 4 3

A: We will determine the cyclic subgroup generated by each element of G

Q: How many subgroups of the group G = (Z30, +30)? O a. 4 O b. 7 O c. 5 O d. 6 O e. 8

A: We know that τ(n) is number of positive divisors of n Also τpaqbrc = (a+1)(b+1)(c+1) , where p , q ,…

Q: order 8 of a group G, and =

A: Given that order of a is 8 .Then  a8=e Rearrange  a little bit , we can have a42=e Hence order of…

Q: How many subgroups in Z/30Z 4 30 6 CO

A: Here we have group z/30z and find its number of subgroups.

Q: ow many subgroups of order 3 does D3 have? Write a number of subgroups only.

A: D3={1 , r , r2 , f , rf , r2f }  Or=3 Of=2    rmf=frn-m   n=3 , 0≤m≤3 O(rif)=2   0≤i≤2 3-order…

Q: How many subgroups are there in Z/14Z?

A: Subgroup: Let (G, ∙) be a group and S be a non‐empty subset of G.Then, S is called a subgroup of G…

Q: How many subgroups of the group G = (Z30, +30)? а. 8 O b. 6 С. 5 O d. 7 O e. 4

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Q: Q/ How many non-trivial subgroups in s3 a) 2 b) 3 c) 4 d) 5

A: The set S3 is given by  S3=e, 12, 13, 123, 132 The subgroups of S3 are e, e, 12, e, 13, e, 23, e,…

Q: How many proper colorings of C15 with color set {1, 2, 3} are there? Hint: find a recursive formula…

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Q: In Z24, find a generator for (21) (10). Suppose that |a] = 24. Find a generator for (a²') n (a!0).…

A: First, we find the values for given generators;

Q: Suppose that a subgroup H of S5 contains a 5-cycle and a 2-cycle.Show that H = S5.

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Q: This is Abstract algebra question: How many subgroups of order 4 does D_4 have?

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Q: What is the numbers group of

A: The given number is 5. The value of 5 is 2.23606...

Q: A subgroup that is representative of a population is called, a. Population O b. A category с. А part…

A: Definition: The total collection of all the elements that we are interested in is called a…

Q: Suppose that G is cyclic and G = (a) where Ja| = 20. How many subgroups does G have?

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Q: let G={e, a, a^2, a^3, a^4, a^5, a^6, b, ab, a^2b, a^3b, a^4b, a^5b, a^6b}. related by the equation…

A: We are given the group, G = {e, a, a2, a3, a4, a5, a6, b, ab, a2b, a3b, a4b, a5b, a6b} related by…

Q: How many non-trivial subgroups in s3 ? a)2 b)3 c)4 d)5

A: The given group is S3 of order 6. The elements of the group can be listed as S3=I,12,13,23,123,132…