4. List the elements of the subgroups (3) and (15) in Z18. Let a be a group element of order 18. List the elements of the subgroups (a) and (a15). Lict tha alamanto e /21 and /7in I20 af the charaun

Q: The subgroups of Z under addition are the groups nZ under addition for n. True or False then why

A: True or False   The subgroups of Z under addition are the groups nZ under addition for n.

Q: is the smallest order of a group that contains both a subgroup isomorphic to Z12 and Z18?

A:

Q: Consider the dihedral group D6.Find the subgroups of order 2,3,4 and 6

A:

Q: The following is a Cayley table for a group G, 2 * 3 * 4 = 3 1 2. 4 主 3. 4 2 1 21 4 345

A: For group, 2*3*4=(2*3)*4.

Q: Find the three Sylow 2-subgroups of D12 using its subgroup lattice below.

A: Given: Using D12's subgroup lattice below, determine the three Sylow 2-subgroups.

Q: C. Find all subgroups of the group Z12, and draw the subgroup diagram for the subgroups.

A:

Q: (c) Prove that the intersection of any three subgroups is a subgroup while the union of two…

A:

Q: Give the subgroup diagram for each of the groups: (a) Z24 (b) Z36-

A:

Q: 2. Determine the number of elements of order 15 in the group Z75 ZL20- Also determine the number of…

A:

Q: Q/ In (Z6 , +6 ) find the cyclic subgroup generated by 1, 2, 5.

A:

Q: Show that S5 does not contain a subgroup of order 40 or 30.

A: Let’s assume that the H is a subgroup of S5. So,

Q: O In a group (G,x), if IGl= 37, the number of Passible Subgroups in G are

A: Note: Since you haven't mentioned which question you would like to get answered. We are providing…

Q: Suppose that H is a subgroup of Z under addition and that H contains250 and 350. What are the…

A:

Q: is a subgroup of Z1, of order: 3 12 O 1 The following is a Cayley table for a group G. 2. 3.4 = 2 3…

A:

Q: 1ABCD E 1 A D E

A: Commutative group of order 6 is z6 under multiplication.

Q: QUESTION 9 Draw the subgroup lattice diagram for Z60

A:

Q: Suppose that H is a subgroup of Z under addition and that H contains 250 and 350. What are the…

A: Given H be a subgroup of (Z,+) containing250 and 350Note that,  GCD(250 , 350)=1⇒by property of GCD,…

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

A:

Q: List the elements of the subgroups and in Z30.  Let a be a group element of order 30.  List the…

A:

Q: Find all inclusion between subgroups in Z/48Z

A:

Q: Every finite group of order 36 has at most 9 subgroups of order 4 and at most 4 subgroups of order 9…

A:

Q: Consider find Subgraup. Dihedral group D- of order 2,3,4 and 6.

A: A group G of two generators x and y of order n and 2 respectively with some relation is called the…

Q: The following is a Cayley table for a group G. 2*5 4 = 1 1 3 1 4 2 4 4. 4. 5. 4. ENG pe here to…

A: 1

Q: Find the three Sylow 2-subgroups of S4

A:

Q: 3. List all elements of the cyclic subgroup of Z12 generated by 5

A: Solving

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

A: 1 25 ∈ Z30    ∴ 025=01ged25,30               =305=6    ∴25 has 6 elements  2 30 ∈ Z42…

Q: List the elements of the subgroups (20) and (10) in Z39. Let a be a group element of order 30. List…

A: Given: Subgroups <20> and <10> of Z30 To Find: The elements of the subgroups <20>…

Q: 4-Let (Z12, +12) be a group and let S={4,6}, find subgroup H generated by S. if exist

A: I have used the definition of subgroup generated by a subset.

Q: 3. How many cyclic subgroups does S3 have?

A: The objective is to find the number of cyclic subgroups of S3. Subgroups of S3 are, H1=IH2=I, 1…

Q: (a) Draw the lattice of subgroups of Z/6Z. (b) Repeat the above for the group S3.

A:

Q: 2- Find the cyclic subgroups in (Z,, +,) generated by 3,5.

A:

Q: Can a group of order 55 have exactly 20 elements of order 11? Givea reason for your answer

A: Any element of order 11 made a cyclic subgroup with 11 elements. These are non-identity elements of…

Q: Draw the lattice of the subgroups Z/20Z.

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: The group (Z6,6) contains only 4 subgroups

A:

Q: Let (Z12, +12) be a group , if we take {0,4,8} for the set H then ({0,4,6}, +12) is evidently a…

A: Let H=0, 4, 6 We know that the operation in ℤ12 is addition. So, the element of left coset is of the…

Q: 2*. Let Q/Z be the group described in problem 12 of Worksheet 1.1. Find list the elements of the…

A: To identify the subgroups generated by the given elements in the quotient group Q/Z.

Q: Consider the discrete group G of order 8 that has the following Cayley diagram e If we have the…

A: The sequence of operations is fcagec. Each element g of G is assigned a vertex: the vertex set…

Q: The group ((123)) is normal in the symmetry group S3 and alternating group A4.

A:

Q: Q2/ In (Z9, +9) find the cyclic subgroup generated by 1,2,5

A:

Q: If H and K are subgroups of G of order 75 and 242 respectively, what can you say about H N K?

A: Solution

Q: The group (Z6,+6) contains only 4 subgroups

A:

Q: Suppose that X and Y are subgroups of G if |X|=28 and |Y|=42, then what is

A: "According to Bartleby Guideline, Handwritten solution are not provided" Given,            |x|=28…

Q: Since 11 is an element of the group U(100); it generates a cyclic subgroup Given that 11 has order…

A:

Q: Obtain al the Sylow p-subgroups of (Z/2Z) X S3

A:

Q: What could the order of the subgroup of the group of order G| = 554407

A: We find the possible order of all the subgroups of the group G, where |G|=55440 by using Lagrange's…

Q: 7. You have previously proved that the intersection of two subgroups of a group G is always a sub-…

A:

Q: (b) Complete the following character table of a group of order 12: 1 3 4 X1 X2 X3 4,

A: The character table of a group of order 12:

Q: Suppose that G is cyclic and G = (a) where Ja| = 20. How many subgroups does G have?

A:

Q: Let c and of d be elements of group G such that the order of c is 5 and the order of d is 3…

A: Need to find intersection of subgroup

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.