Question 5 Consider the factor group (Z, x Z,)/(1,1). (a) What is the order of the factor group? (b) What is the identity element of the factor group? (c) What is the order of (1,2)+((1,1)) in the factor group?

Q: give the order of the element in the in the factor group (2,5) + in (Z3 x Z6)/

A:

Q: Show that a group of order 132 is not simple.

A: A group G is said to be simple if it has no normal subgroup other then e and G itself. Moreover, if…

Q: Find the order of the given elements in the factor groups. (a) 7+ (3) in Z15/(3). (b) (3, 1) + ((1,…

A: a) we need to find the order of the element 7+<3> in ℤ15/<3> Since,…

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: 7 How do i derive the quadratic and cubic functions from the point group

A: Given information: Quadratic function from the point group. Note: - As per guidelines we will solve…

Q: 12. Prove that the following groups are not cyclic: (a) Z2 x Z2 (b) Z2 x Z (c) Z x Z.

A: To show the following groups are not cyclic. If a group is cyclic the there exit an element in that…

Q: Find the factor group G divides H where G is the quaternions,H=Z(G)

A:

Q: Which one of the following is not a group? (1): (8Z,+) where 8Z = {8n | n € Z} (2): (Z8, +) where…

A:

Q: What is the relationship between the order of a group and the order of its elements in abstract…

A: In abstract algebra, a "group" is a set of elements combined with an operation that satisfies four…

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: Being N { 0, 8, 16a)culate the order of 10 Nin the factor group (Z24, +) /!N

A:

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

A:

Q: (B): Let (G,) be the group define by G= ka.b):a,be R', az0} and the operation on G define by (a,b)…

A: Our guidelines we are supposed to answer only first three subpart of the question. Kindly repost…

Q: The factor group U(16)/(9)has an element of order 4. True of false?

A:

Q: Suppose that G is a group that has exactly one non-trivial proper subgroup. Prove that G is cyclic.

A:

Q: inf (A) Give the example that group A is not null and -00 = and (sup (A) = max (A). %3D <י(S

A: Let  A=-n where n∈N  A is not null inf(A)=-∞sup(A)=-1=max(A)

Q: 1. Let G = Z/36Z. (a) Find all subgroups of G, describe all containments between these subgroups,…

A:

Q: How do you interprete the main theorem of Galois Thoery in terms of subgroup and subfield diagrams?

A:

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

A:

Q: Find all non-trivial direct factorizations of (1) the four-group (V={e, (12)(34), (13)(24),…

A: Please find the answer in next step

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: Let G ={(: :) a : a – b = c – d, a, b, c, d E R d Show that G is a group under (the usual) matrix…

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…

Q: (b) what is the Signiticance ot Factor groups? ds there ance

A: Part-I: A factor group is a mathematical group obtained by aggregating similar elements of a larger…

Q: Which of the following is group under multiplication? (A) Q (B) Q-{0} (C) Q-{1} (D) Q-{0,1}

A: