what will be the class equation of a group of order 12? In general what steps do we follow to find class equation of  group of order n?

Q: Give an example of a group of order 12 that has more than one subgroupof order 6.

A: Consider the group as follows, The order of a group is,

Q: group. What do you mean by conjugate elements and classes? Find the classes of the (Rohilkhand 1999)…

A: In the given problem, the definition of 'conjugate' elements and classes in a group are used. Find…

Q: The group (Z4 ⨁ Z12)/<(2, 2)> is isomorphic to one of Z8, Z4 ⨁ Z2, orZ2 ⨁ Z2 ⨁ Z2. Determine…

A: Consider the group elements, Here the order of K is 6. Consider the order of group, The order of G…

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=…

A:

Q: . Consider the group (Z30, +). (a) Find the orders of the elements 3, 5, 6, 7,8, 18, 19, 24 and 25.…

A: The order of an element is n , when n is the least such that, n.a=0 3.10 = 0 and 19 the least , so…

Q: Which of the following groups are cyclic? For each cyclic group, list all the generators of the…

A:

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

A: using  third Sylow Theorem

Q: Is S3 x S3 group (the direct product of symmetric group S3) nilpotent?

A: Given question:   Is S3 x S3 group (the direct product of symmetric group S3) nilpotent?

Q: Which of the following groups are cyclic? For each cyclic group, list all the generators of the…

A: To identify the given group is cyclic or not.

Q: Find the order of the given factor group (Z3 x Z6)/

A: If G be a group, and H be a subgroup of G, then the order of the factor group G/H is given by…

Q: Which of the following vectors in R³ is orthogonal to the vector ?

A:

Q: Show that there are no simple groups of order 255 = (3)(5)(17).

A:

Q: Q 5 Find the inverse of the element 9 in the group (U(10), ®10). Q 6 Find the order of the element 2…

A:

Q: which of the following group are cycle ?(a) U(35) (b)U5(40)

A: It is required to check which of the given group are cyclic. (a) U(35) (b)U5(40)

Q: What is the order of the group  ℤ10 x  ℤ15 x U(10) /〈(9, 10, 7)〉?

A: To determine the order of the group ℤ10 × ℤ15 × U(10) / 〈(9, 10, 7)〉, we need to divide the order of…

Q: A school psychologist designed a study to investigate the effectiveness of three study programs. A…

A: A sample of 30 students were randomly selected and assigned to one of the three programs. Here…

Q: X={1,2,0,,8,3,5}. (a) Find all possible permutations and show that its form a group. (b) Find its…

A: Note: According to our guidelines We’ll answer the first 3 subparts of the question since the exact…

Q: Determine the class equation for non-Abelian groups of orders 39and 55.

A: We have to determine the class equation for non-Abelian groups of orders 39 and 55.

Q: True or False:  No group of order 21 is simple.

A:

Q: Find all the producers and subgroups of the (Z10, +) group.

A: NOTE: A group has subgroups but not producers. Given group is ℤ10 , ⊕10 because binary operation in…

Q: Find S4/N elements and show that they can be combined into a group. N={e,(23),(234),(243),(12)(34),…

A: We know,      | S4 | = 4! = 24     | N | = 12   So, | S4/N | = | S4 |/| N |                      =…

Q: (d) Find the cosets of the quotient group (5)/(10), and determine its order.

A:

Q: Find all the generators of the following cyclic groups: (Z/6Z,+), ((Z/5Z)*, ·), (2Z, +), ((Z/11Z)*,…

A:

Q: (4) Chapter 2, exercise 6.9: Prove that a group and its opposite group Go (Exercise are isomorphic.

A: (4) Chapter 2, exercise 6.9: Prove that a group and it's opposite group G°  is isomorphic

Q: List the elements of the quotient groups of (a) (4Z, +) in (Z, +) (b) Z30/(6) (c) Z30/(J/H), where J…

A: Quotient group GH ={ Ha | a∈ G} where H is normal subgroup of group G. Here al given groups are…

Q: Write out the Cayley table for the group {1, -1, i, -i} under multiplication where i = sqrt(-1). (In…

A:

Q: A = {1, 2, 3, 4) and S4 = {f | f : A A, one-to-one and orten} group (S4, ) be given. In the S4 k…

A: The question can be transformed as follows. We have to find all elements of order 2 in S_4

Q: Suppose a group contains elements of order 1 through 9. What is the minimum possible order of the…

A: We know that, Order of the given group is divisible by natural numbers 5,7,8 and 9. So the least…

Q: Show that a group of order 12 cannot have nine elements of order 2.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Find the order of the given factor group (Z8 x S3)/

A:

Q: Find the order of the element 2+ (6) in the group Z30/(6).

A:

Q: give the order of the element in the factor group (2,0) + in (Z6 x Z8)/

A: Let    G be a group, and let    g be an element of that group.The order of the element   g, denoted…