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

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

A: Solution:-

Q: Show that the cyclic group of n objects, Cn, may be represented by r", m = 0, 1, 2,...,n– 1. Here r…

A: Given  Cn is a cyclic group of n elements To show Cn is generated by some element r of Cn. That is…

Q: C. Find the number of elements in the indicated cyclic group. 1) The cyclic subgroup of Z30…

A: Given: The cyclic subgroup of 230 generated by 25. To find the number of elements that is indicated…

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A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: o:Z, →Z, A GROUP HOMOMORPHISM 30 30 KER () = {0,5,10,15, 20, 25} o(13) = 6 now THAT, 0" (6) FIND ?

A:

Q: Which of the following is the identity element in the group Z/14Z × µs O (147,0) O (142,1) O…

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Q: 9. Which of the following groups are cyclic? Justify your answer. a) Z;×Z12 b) Z1,×Z, c) Z2×Z8×Z16…

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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: 10. Let E = Q(V2, V5). What is the order of the group Gal(E/Q)? What is the order of Gal(Q(V10/Q)?

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Q: Q1) Consider the group Z10X S5. Let g = (2, (345)) € Z10X S5. Find o(g). T LOV

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: If U(14) = , then U(14) is cyclic group generator by a) 5 b) 11 c) 4 d) None of the above

A: We have to solve given problem:

Q: 6.10 Find all subgroups of Z,XZ4. 6.11 Find all subgroups of Z,xZ,>

A: To find  All subgroups of z2*z4

Q: Let G be a group of order n. For what value of n is the group G NOT cyclic?

A:

Q: The following is a Cayley table for a group G. The order of4 is: 2 1 3 3 4 1 4 1 4 1 5. 2 512 m 45…

A: By observing the Cayley table :

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

A:

Q: 6. Complete the multiplication table for the group G = {a, b, c, d} a d a b d

A: QuestionDetails: Part of the multiplication table forthe group G = {a,b,c,d} is given. Complete the…

Q: 2. In each case determine whether the two given groups are isomorphic. Justify your answer. a) (2Z,…

A: a) Given that the groups are 2ℤ,+ and 3ℤ,+.The function is given by φ:2ℤ→3ℤ and can be defined as…

Q: 1. Construct the multiplication table for the the group Us = {1,a, a², a°, aª} where a = 2ni e 5

A: As per our guidelines we are suppose to answer only one ques. Answer of question 1 is as follows:

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: Let E = Q(√2, √5). What is the order of the group Gal(E/Q)?What is the order of Gal(Q(√10)/Q)?

A:

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: 0:Z, →Z, A GROUP HOMOMORPHISM KER () = {0,5,10,15, 20, 25} o(13)= 6 now THAT, o" (6) FIND ?

A:

Q: If H and K are subgroups of G, |H|= 16 and |K|=28 then a possible value of |HNK| is * O 6 16 8. 4

A: Order of an subgroup should divide order of an group. Intersection of two subgroups again a…

Q: Consider the group D4

A: Given: Group D4=a,b=e=1,a,a2,a3,b,ab,a2b,a3b and a=1 2 3 4, b= 2, 4 To find : The value of…

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

A:

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: If H and K are subgroups of G, |H|= 16 and |K|=28 then a possible value of |HNK| is * 8. O 16 4 O 6

A: Since you have posted multiple questions only the first question will be answered. It is given that…

Q: Write out the Cayley table for the dihedral group D6 = {1,r,r2,s,sr,sr2}. (In general, we apply the…

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Q: If U(14) = ,then U(14) is cyclic group generator by a) 4 b) 11 c) 3 d) None of the above

A: We have to find the generator of U(14)

Q: 4

A: To identify the required cyclic subgroups in the given groups

Q: 6.2 Which of the following groups are cyclic? a) Z12×Z, b) Z10x Zgs c) Z4xZ2sx Z, d) Z22XZ21 xZ6s

A:

Q: If H and K are subgroups of G, |H|= 16 and |K|=28 then a possible value of |HNK| is 8 O 16 4 6

A: Answer is 4.

Q: Consider the group (U(20), '20). 1. What is (7 ·20 13)-1? 2. Solve for x in the equation x '20 9 =…

A: Unitary group, multiplication madulo

Q: ng to a group. If |a| = 12, |6| = 22, and (a) N (b) # {e}, prove that a® = b'1.

A:

Q: Q 5 The order of the element (123) of the group (S3,0) is (a) 1 (b) 2 (c) 3 (d) 00 Q 6 The order of…

A: Q.5. order of (123) in (S3,∘) is 3 (option (c) is true). since (123)∘(123)∘(123) = (123)∘(132) =…

Q: 1. Which one of the following groups, under addition, is cyclic? (a) Zz x Z12 (b) Z10 x Z15 (c) C…

A: Solution

Q: In proving that G/N is a group where do we first use the fact that N Is ha Select one: a. The invers…

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Q: (Identity) element for the group {Z, +} is 1. T

A: Ans:     F The given statement is "Identity element for the group Z,+ is 1" check whether this is…

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

A: The subgroups of are such that n is a divisor of 36 .

Q: need help with cyclic groups plz, thanks

A: Given groups are,

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

A:

Q: If H and K are subgroups of G, H|= 16 and |K|=28 then a possible value of |HNK| is * 4 О 16 6 00 ООО…

A:

Q: Which of the following groups are isomorphic? i) Z/75Z ii) Z/3Z ® Z/25Z iii) Z/15Z @ Z/5Z iv) Z/3Z @…

A: Groups (i) ℤ/75ℤ and (ii) ℤ/3ℤ⊕ℤ/25ℤ are isomorphic. Groups (iii) ℤ/15ℤ⊕ℤ/5ℤ and (iv) ℤ/3ℤ⊕ℤ/5ℤ⊕ℤ/5ℤ…

Q: Suppose that a group G has order 8, but is not cyclic. Then that g for all g e G Select one: а. 1 3…

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Q: Decide which of the elements 2,3, and 5 are generators of the group Z/6

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

A:

Q: Q1/ (True or False): Let G= (o, 1); then (G,+) is group ?

A: We have to check

Q: For G = (Z5 ,+s) , how many generators of the cyclic group G? 5.a O 1.b O 3.c O 4.d O 2.e O

A: