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

Q: An is the alternating group on n letters. What is |An|?

A:

Q: for each of the group Z2,Z4,Z6 INDICATE WHICH CYCLIC. FOR those cyclic list  all the generators?

A:

Q: Ann is a risk averse individual with the utility function u(w) = w1/2. Her current wealth is $300…

A:

Q: What is the minimum number of generators needed for Z2 ⊕ Z2 ⊕Z2? Find a set of generators and…

A: In this question, we have to find the minimum number of generators needed for the group  ℤ2⊕ℤ2⊕ℤ2…

Q: Exercises 3(a) Prove that the groups $ and D6 are isomophic ; (e) Preve that the additive and the…

A:

Q: In the group S6, consider the elements 1 2 3 4 5 6 4 3 6 5 1 2 1 2 3 4 56 35 4 2 6 1 a = and B = (a)…

A:

Q: Determine the conjugacy classes of Ag and the class equation for Ag.

A: Conjugacy relation:  Let G be a group and ~be a relation on group G given by b~a if and only if b is…

Q: (3) What is the order of (8,2, 5) in group Z12 × Z6 × Z7. (For this question, I don't need a strict…

A:

Q: If a, b, and c are group elements and |a| = 6, |b| = 7, express(a4c-2b4)-1 without using negative…

A:

Q: The inverse of each element in the group ({1, 3, 5, 7}, ∙8)

A:

Q: . In the group (Z19 – {ô}, -19), Find the inverse of the following elements. 2 11 (LO

A:

Q: Q2: If G = R- {0} and a * b = 4ab ,show that (G,*) forms a commutative group? %3D

A: To show for the commutative group of (G, *), we verify the following properties of the commutative…

Q: Z12 The order of the element 5+ (4) in the factor group is (4) a) 12 b) 5 c) 4 d) 0

A:

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

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: Suppose that <a>, <b> and <c> are cyclic groups of orders 6, 8, and 20,…

A:

Q: Que 327: Let X, Y be cyclic groups of order 2,3 respectively. Find the orders of the elements of…

A: Let X, Y be cyclic groups of order 2,3 respectively then we have to find the   the orders of the…

Q: Write down the six elements of S3 and give the multiplication table for the group. The six elements…

A: Given six elements of S3 are     1=123123, a=123231=123 , b=123312=132, c=123213=12, d=123321=13,…

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

A:

Q: 3 In the group (S5, o), (142) o (123)= ....

A: The above problem can be solved as follows:

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

A:

Q: Show that (4Z) (6Z) is a commutative group.

A: Defintion:A group is said to be commutative if  for all .Theorem:The finite cartesian product of…

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

A:

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: