Give an example of a group with 105 elements. Give two examples of groups with 44 elements.

Q: We have a group of 10 students that we want to partition into two sub-groups. None of the two…

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Q: What is/are the mode(s) of this group of numbers? (4, 6, 9, 5)

A: Mode: Mode is the value, which has the highest frequency among all other values of the observation.

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

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Q: When do you use a t-test for independent groups and what do the numerator and deniminator in the…

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Q: Let G= How many elements does G have?  To what familiar group is G isomorphic?

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Q: Which of the following does not belong to the group? 3 6. 4 8. 10

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Q: take the groups Z4 and Z5, what will be the elements of Z4 x Z5?

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Q: mat do you call a group that is commutative?

A: A detailed solution is given below.

Q: 11. Prove that every Cayley table is a Latin square for a group. That is, each element of the group…

A: To prove, each element of the group appears exactly once in each row and each column of a Cayley…

Q: Show that the set of rational numbers (positive and negative fractions) together with multiplication…

A: The set under question can de defined as S={pq|p∈ℤ,q∈ℤ,q≠0}We have to show that Set S along with…

Q: 9. What's the difference between the order of a group and the order of element of a group?

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Q: Construct the group table for A4.

A: S4 is the set of all permutations on the set of four elements namely {1,2,3,4}. Then A4 is the set…

Q: What is the name for the group of quadrilaterals for whom all four angles are 90° (and no other…

A: Group of quadrilaterals for whom all four angles are 90°.

Q: Is the set of numbers described below a group under the given operation? Whole numbers; addition ...

A: Introduction: A group is defined as a set that has a binary operation that allows any two elements…

Q: Write the group table for Z₂ XS2.

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Q: In practice, what can be the differences between the relationships of two pairs of groups, knowing…

A: Homomorphism -  It is  algebraic term for a function having some algebraic operations. For a group…

Q: If a,b are elements in a group and a-2, b-3. them Ka)N(b=6

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Q: True or false? In the group (S3, ◦), (132)^−2 = (123).

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Q: How many different groups can be formed for arranging 11 books on a bookshelf?

A: first book can be arranged =11 second book can be arranged =10 third book can be arranged =9 .. ..…

Q: Give an example or explain why the following is not possible.  An infinite group that is finitely…

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Q: How many elements does the group of rotations of a regular hexagon have?

A: The group of rotations of a regular hexagon is D6. And as the order of the group Dn is 2n.

Q: If a1, a2, . . . , an belong to a group, what is the inverse of a1a2 . . . an?

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Q: Find the elements in the alternating groups A3, and A4, respectively.

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Q: Is the set Z* under addition a group? Explain. Give two reasons why the set of odd integers under…

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Q: Please explain an infinite p-group, and give an example

A: Infinite p-group: Infinite p-group is an infinite group in which the order of every element is a…

Q: Is the set of numbers described below a commutative group under the given operation? Whole numbers;…

A: This is a problem of Abstract Algebra.

Q: 9. In a group, prove that (a"')"' - a

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Q: order 8 of a group G, and =

A: Given that order of a is 8 .Then  a8=e Rearrange  a little bit , we can have a42=e Hence order of…

Q: Consider the groups  and .

A: We have to consider the groups

Q: Is the set of numbers described below a group under the given operation? Whole numbers; addition ...…

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Q: How many subgroups of the group G = (Z30, +30)? а. 8 O b. 6 С. 5 O d. 7 O e. 4

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Q: 16. A class consist of 15 men and 20 women, in how many ways can a group of 5 be formed if it has to…

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Q: In a group G, the law ab-Dac implies b-c is called..

A: Answer : 1 right cancelation law

Q: Determine the number of permutations of 2 members of a group from a group with 6 members.

A: Given n=6 r=2

Q: The order of the element (1,1) + ((4,4)) in the factor group Z, × Z,/((4,4)) is 6. Select one: True…

A: Given statement is, " The order of the element 1,1+4,4 in the factor group  ℤ6×ℤ84,4 is 6. " The…

Q: 3. How many groups van can be formed from 8 students taking at least two at a time?

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Q: Find all the elements of a factor group Z3 X Z4 /

A: We have to find the all the elements of a factor group ℤ3×ℤ4/2,2 Let the group H=ℤ3×ℤ4 Then order of…

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

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Q: A group G with four elements has the following partially-filled Cayley table. In particular, a² = c,…

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Q: The elements of the quotient group (2/8). 12 (0,1,2,3,...,8) 1- 2- -208,-108,008,108,208,...) 3- 4-…

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Q: Let G=.  How many elements does G have?  To what familiar group is G isomorphic?

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Q: How many groups can be formed from 8 studenta taking at least 2 at a time?

A: nCr=n!(n-r)! r !No of ways of selecting r from nis nCr

Q: 4) A treasure chest contains 10 rubies and 8 diamonds. In how many ways can a group of six jewels be…

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Q: In a group of 4 people, is it possible for each person to have exactly 3 friends? Why?

A: Let G be a graph with 4 vertices, one vertex representing each person in the group. Join two…

Q: What can you say about the centre of a simple group?

A: 9

Q: True or false? Every group of 125 elements has at least 5 elements that commute with every element…

A: Let G be a group whose order is 125 ⇒G=125=53 Center of a group G ( ZG ) is the set of all those…

Q: How to complete the table using the binary operation as a group? Let, S={f,g,h,j}, and let the…

A: Given the set

Q: Is the set of numbers described below a commutative group under the given operation? Whole numbers;…

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Q: There are six persons in an office. A group consisting of three persons has to be formed. In how…

A: Total person in office (n) = 6 A group consisting of three persons(r)=3 By using combination   ncr…

Q: 15. From 9 different books of which 3 books are about Mathematics, how many groups of 5 books each…

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