a) How many subgroups does (Z10,O) have? What are they? b) How many subgroups does (Z74,Ð) have? What are they?

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

A: To find Number of  cyclic subgroups does U(15) have

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

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Q: Find all the conjugate subgroups of S3, which are conjugate to C2 .

A: Given-S3 To find- all the conjugate subgroup of S3 which are conjugate

Q: Which among is a non-cyclic group whose all proper subgroups are cyclic? U(12), Z8 , Z, U(10)?

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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: Let G be group, aeG ond lal=n. Show that laml = (m,n) %3D

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Q: · In a group, prove that (ab) = b-'a-|

A: As you asking for question number 7 , I solve for you.

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

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

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Q: If we have 6 subgroups as 36.2,37.0,39.6 41.02,44.3 , and 45.5. Graph Z and MW charts and plot the…

A: A z-mR control chart is two charts.  One chart is for the z value which is the “standardized” X…

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

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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: Determine the number of elements of order 15 and the number ofcyclic subgroups of order 15 in Z30 ⨁…

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Q: Show that S5 does not contain a subgroup of order 40 or 30.

A: Let’s assume that the H is a subgroup of S5. So,

Q: Find all subgroups of U(7)

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Q: many

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

Q: In a group G,let a,b and ab have order 2.show that ab=ba

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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: Suppose that H is a subgroup of Z under addition and that H contains 250 and 350. What are the…

A: Given H be a subgroup of (Z,+) containing250 and 350Note that,  GCD(250 , 350)=1⇒by property of GCD,…

Q: The group of of a regular n- sided polygon is called the dihedral group of order 2n.

A: Given statement is " The group of           of a regular n-sided polygon is called dihedral group of…

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

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

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Q: A square has four rotational symmetries (including the identity) and four line symmetries. Make 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: Consider find Subgraup. Dihedral group D- of order 2,3,4 and 6.

A: A group G of two generators x and y of order n and 2 respectively with some relation is called the…

Q: Find the three Sylow 2-subgroups of S4

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

A: The explanation of the solution as follows:

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: If H and K are normal subgroups of G, show that their intersection is also a normal subgroup. To do…

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Q: 5. D, =

A: First we have to show that the dihedral group is  D_2n is solvable for n>=1

Q: ake the minimum three groups along with subgroups (Mathematically) and verify the langrage theorem

A: Lagrangian theorem says that, If H is a subgroup of a group G then H\G. Now take, Z3={0,1,2} The…

Q: At now how many elements can be contained in a cyclic subgroup of ?A

A: There will be exactly 9 elements in a cyclic subgroup of order 9.

Q: 3. How many cyclic subgroups does S3 have?

A: The objective is to find the number of cyclic subgroups of S3. Subgroups of S3 are, H1=IH2=I, 1…

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: 4. Which of the groups U(14), Z6, S3 are isomorphic?

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Q: The group (Z6,6) contains only 4 subgroups

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Q: Q/ How many non-trivial subgroups in s, ?

A: For the given statement

Q: The group (Z6,+6) contains only 4 subgroups

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Q: Represent the symmetry group of an equilateral triangle as a groupof permutations of its vertices

A: To determine: The symmetry group of an equilateral triangle as a  group of permutations of its…

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: Create Cayley table for square isometry groups

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

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Q: Find the outer set of points for group S.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: The group (Z, t6) contains only 4 subgroups

A: