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

Q: 54 The groups An and Sn are not solvable for all n ≥ 5.

A: Solution:-

Q: Suppose the Cayley table for B = {e, a, b, c}unde the binary operation * is given by * е а b е е аb…

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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: 4. The permutations (e, a, B, v) form a group. If e = (1)(2)(3)(4)(5)(6), a = (1)(2)(35)(46), B=…

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Q: How many subgroups of order 4 does D4 have?

A: Solution: Assume the following dihedral group D4, The above group consists of three subgroups of…

Q: G is Klein's 4-group%3D{e,a,b,c}, H=, then [G:H] is 3 4 O 1 O 2 None of them

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Q: Which of the follewing is a group? The set of non-zero real numbers under division. The set…

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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 non-trivial subgroups in S3? 3 4 2.

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Q: In the group Zg compute, (a) 6 + 7, and (b) 2-'.

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Q: Which of the following elements in Z8000000 is not of order 8? 7 000 000, 2 000 000, 3 000 000, 5…

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

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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: List the cosets of each subgroup: a. (8) in Z24 b. (3) in Us

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Q: Let p1, p2 ......pn be distinct primes. Up to isomorphism, how manyAbelian groups are there of order…

A: Given Data The distinct prime is p1, p2…………. pn.   The number of Abelian groups of the order pm, so…

Q: many

A: We have to find the number of generator of the given group of order

Q: 12. Find all subgroups of Z2×Z4.

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Q: How many elements of order 5 might be contained in a group of order 20?

A: using  third Sylow Theorem

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: 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: How many subgroups in Z/40Z None of them 10 40 8

A: Solution: here the group Z/ 40Z is given, which is  isomorphic to Z/ 40Z . since Z/ 40Z is a…

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: O Find Subgroup of order a, 3,4 and 6

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Q: How many subgroups of a

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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: How many elements of a cyclic group with order 14 have order 7?

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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: 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: (i) What is the order of the group ? (ii) How many characters are missing ? (iii) Find the missing…

A: From the given congruency classes. (i) The aim is to find the order of the group. Using congruency…

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: 13. Find groups that contain elements a and b such that |al = \b| = 2 and a. Jab| = 3, b. Jab| = 4,…

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Q: How many subgroups does z/60z have? Find all generators of the subgroups of z/60z and there…

A: According to the given information first it is required to find the number of subgroups of

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: If H and K are subgroups of G, |H|= 16 and IK|=28 then a possible value of |HNK| is * O 16 6. 4 O O…

A: H and K are subgroups of G H=16 and K=28 we have to find the possible value of H∩K

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

A: Note: We are using the simple procedure that is by direct calculation. We are given the group S4 and…

Q: If H and K are subgroups of G, |H|= 18 and |K]=30 then a possible value of |HOK| is O 4 O 18 O 8

A: Given that H and K are sub-group of G.                  |H|= 18                  |K|=30 To find…

Q: How many Sylow 3-subgroups of S5 are there? Exhibit five

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Q: 3= {m + nV5| m * EZ}CR. ca> Show that s is a subgroup ob (R, +), (6) Show that ib sl, st ES then…

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Q: If H and K are subgroups of G, |H|= 20 and |K]=32 then a possible value of IHNKI is O 2 16

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Q: How many cyclic subgroups of order 2 in Zg O Z2 4 None of them 2 1 3

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Q: It is known that C6 = {r € C | r° = 1} is cyclic. Find all possible generators.

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Q: Construct the distinct left cosets of the subgroup {(1), (1,3,2), (1,2,3)} in S3.

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Q: Express the permutation (2 4 5)(1 3 5 4)(1 2 5) as a single cycle or a s a product of cycles and how…

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

A: D4 has 8 elements:. {1, r, r2, r3, d1, d2, b1, b2,}. where r is the rotation on 90◦, d1, d2 are…