Prove that if (ab)' = a*b² in a group G, then ab = ba.

Q: Prove that a group of order n greater than 2 cannot have a subgroupof order n – 1.

A: Given: To Prove: G cannot have a subgroup of order n-1.

Q: In (Z12, +12) , H, = {0,3,6,9} and H2 = {0,3} are tow subgroups of the group (Z12, +12), but (H, U…

A: We have given   H1=0,3,6,9 and H2=0,3 are two subgroups of the group Z12, +12. We can see here…

Q: Prove or Disprove: If (G, *) be an abelian group, then (G, *) a cyclic group?

A: If the given statement is true then we will  proof the statement otherwise disprove we taking the…

Q: Prove that every group of order 330 is not simple.

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Q: 8. Show that (Z,,x) is a monoid. Is (Z,,x4) an abelian group? Justify your answer

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Q: Prove that a group of order 7is cyclic.

A: Solution:-

Q: 9. Prove that a group of order 3 must be cyclic.

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Q: Prove O3 is not a group

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Q: 3. Prove that (Z/7Z)* is a cyclic group by finding a generator.

A: Using trial and error method, seek for an element of order 6.

Q: · In a group, prove that (ab) = b-'a-|

A: As you asking for question number 7 , I solve for you.

Q: Prove A3 is a cyclic group

A: We know that If G be a group of prime order then G is cyclic group

Q: 1. What are the generators of the group Z60?

A: We have to find the generator of the group ℤ60

Q: Prove or Disprove that the Klein 4-group Va is isomorphic to Z4.

A: The statement is wrong.

Q: does the set of polynomials with real coefficients of degree 5 specify a group under the addition of…

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Q: The group GLQ,R) abelian group is an

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Q: Let F denote the set of first 8 fibanacci number .Then convert F into a non abelian group by showing…

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Q: How many nonisomorphic abelian groups of order 80000 are there?

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Q: Give an example of elements a and b from a group such that a hasfinite order, b has infinite order…

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Q: Prove that the group of positive rational numbers, Q+, under multiplication is not cyclic.

A: Group under addition cyclic or non cyclic

Q: prove that Every group oforder 4

A: Give statement is Every group of order 4 is cyclic.

Q: Determine all cyclic groups that have exactly two generators.

A:

Q: Prove that the set of natural numbers N form a group under the operation of multiplication.

A: The set N of all natural numbers 1, 2, 3, 4, 5... does not form a group with respect to…

Q: What are the three things we need to show to prove that an ordered pair is a group?

A: We have to give the properties of an ordered pair to prove that it is a group.

Q: Compute the center of generalized linear group for n=4

A: To find - Compute the center of generalized linear group for n=4

Q: Is it possible to find a group operation e on a set with 0 elements? With 1 element? Explain why or…

A: The question is :: is there possible to find a group operation on a set of 0  element? Or with 1…

Q: Prove that in a group, (a-1)-1 = a for all a.

A: By definition (a-1)-1=a are both elements of a-1. Since in a group each element has a unique…

Q: Give three examples of groups of order 120, no two of which areisomophic. Explain why they are not…

A: Let the first example of groups of order 120 is, Now this group is an abelian group or cyclic group…

Q: Prove that a cyclic group with even number of elements contains ex- actly one element of order 2.

A: The solution is given as

Q: Prove that a group of even order must have an odd number of elementsof order 2.

A: Given: The statement, "a group of even order must have an odd number of elementsof order 2."

Q: Let p be a prime number and (G, *) a finite group IGI= p?. How can you prove that the group (G, *)…

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Q: Prove that in a group, (a-1)¯' = a for all a.

A: To prove that in a group (a-1 )-1=a for all a.

Q: The group Cs3,0) is normal group solvable ?

A:

Q: At now how many elements can be contained in a cyclic subgroup of ?A

A: There will be exactly 9 elements in a cyclic subgroup of order 9.

Q: Prove that if (ab)2 = a?b? in a group G, then ab = ba %3D

A: A group is a set with a binary operation with following axioms satisfied. First the operation must…

Q: 2. Prove that a free group of rank > 1 has trivial center.

A: Given:Prove that a free group of rank>1 has trivial center

Q: determine whether the binary operation * defined by a*b=ab gives a group structures on Z. if it is…

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Q: Theorem: Any non-commutative group has at least six elements

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Q: Example: Show that (Z,+) is a semi-group with identity

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Q: Prove that An even permutation is group w.y.t compostin Compostin function.

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Q: Characterize those integers n such that the only Abelian groups oforder n are cyclic.

A: According to the question,

Q: 2. Is the set Z3 = {0,1,2} form a group with respect to addition modulo 3 how about to…

A: We use caley's table to verify the properties of a group.

Q: not

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Q: QI/AI Prove that the mathematical system (s), where (o) is an usual composition map is a group? B/…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (A) Prove that, every group of prime order is cyclic.

A: Let, G be a group of prime order. That is: |G|=p where p is a prime number.

Q: Show that group U(1) is isomorphic to group SO(2)

A: See the attachment.

Q: Prove that a finite group is the union of proper subgroups if andonly if the group is not cyclic

A: union of proper subgroups  proof: Let G be a finite group. In the first place, we are going the…

Q: Consider the set of permutations V = {(1), (1 2) (3 4), (1 3) (2 4), (1 4) (2 3)}. Determine whether…

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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: The set numbers Q and R under addition is a cyclic group. True or False then why

A: Solution

Q: Find the outer set of points for group S.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.