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

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: In (Z13, +13) the set K = {0,3,5,8,9,11} is eyclie subgroup. True False

A: Use the definition and properties of a cyclic group. Check whether the whole group can be generated…

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

A:

Q: (a) What element in G is a2022? (b) What is the inverse of a83? (c) Which elements in G have order…

A:

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: 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: (a) In S4, find the subgroup H generated by (123) and (23) (b) For o = (234), find the subgroup oHo

A:

Q: An event organizer is planing a programme for a group of 20 people who want to embark on a…

A: a) The different partitions are there if the fourth subgroup is made up of 6 people The number of…

Q: An event organizer is planing a programme for a group of 20 people who want to embark on a…

A: a) The different partitions are there if the fourth subgroup is made up of 6 people The number of…

Q: If H and K are subgroups of G, |H|= 18 and |K]=30 then a possible value of |HNK| is 8. 6. 18 4.

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: 12. Find all subgroups of Z2×Z4.

A:

Q: An event organizer is planing a programme for a group of 20 people who want to embark on a…

A: a) The different partitions are there if the fourth subgroup is made up of 6 people The number of…

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: 5. If H = 122Z and K = 8Z are subgroups of (Z, +). Then H + K = ... %3D

A:

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

A:

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

A:

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: Which of the following cannot be an order of a subgroup of Z12? 4 3 Option 4 12

A:

Q: 4. What's mean by a group? Is every group commutative? Explain your answer.

A:

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: How many groups are there of order 12 (up to isomorphism) 5 O None of them 2 O 4 O 8 0

A: Use the concept of isomorphism.

Q: 6.2 Which of the following groups are cyclic? a) Z12×Z, b) Z10×Z85 c) Z4xZ25x Z, d) ZnxZ2 x Z65 -21

A:

Q: How many subgroups of a

A:

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

A:

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 generators does a cyclic group G of order 125 have? A) 100 В) 1 C) 101 D) 11

A:

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

A:

Q: Review the normal subgroups N = {(1), (1 2 3), (1 3 2)} of S3. From these subgroups and groups,…

A: This is a problem of Group Theory.

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

A:

Q: (Z., +6) is a subgroup of (Zg, +8)

A:

Q: Suppose G is a cyclic group with an element with infinite order. How many, elements of G have finite…

A:

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

A:

Q: An event organizer is planing a programme for a group of 20 people who want to embark on a…

A: (a)  The different partitions are there if the second subgroup is made up of 4 people     The number…

Q: • 2. List the elements of the subgroups (1) , (2), (3),(4), (6) and (0) in Z12.

A:

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

A:

Q: Find the order of the element 5(9)in the factor group U(16)/(9).

A:

Q: An event organizer is planing a programme for a group of 20 people who want to embark on a…

A: a) The different partitions are there if the fourth subgroup is made up of 6 people The number of…

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

A:

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…

Q: (a) What element in G is a2022? (b) What is the inverse of a$3? (c) Which elements in G have order…

A: