How many elements of a cyclic group with order 14 have order 7?

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

A: Given: Group, Z2⊕Z2⊕Z2To find: The minimum number of generators and a set of generators and…

Q: Imagine  Z9* a cyclic group. What is order of an element a=2 and show the elements? Show all your…

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Q: How many elements of a cyclic group with order 10 have order dividing 5?

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Q: Give an example of a p-group of order 9.

A: Given, Give an example of a p-group of order 9.

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: Which of the following groups are cyclic? For each cyclic group, list all the generators of the…

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Q: Explain why the only simple, cyclic groups are those of prime order.

A: Proof: Let G be a simple group with |G|>1. We want to prove that G is a cyclic group of prime…

Q: Suppose that a group of order 8 has exactly five elements of order 2.Identify the group.

A: Abstract Algebra, Dihedral group

Q: Analyze the properties of Zs with multiplication modulo 6 to determine whether or not this operation…

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Q: How many elements of order 5 might be contained in a group of order 20?

A: using  third Sylow Theorem

Q: How many elements of the cyclic group GF(81)* are generators?

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Q: If a group has exactly 24 elements of order 6, how many cyclic subgroupsof order 6 does it have?

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

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Q: Which of the following groups are cyclic? For each cyclic group, list all the generators of the…

A: To identify the given group is cyclic or not.

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: The number of generators of a cyclic group of order 213 is * 48 24 144 140

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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: Alte

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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: True or False:  No group of order 21 is simple.

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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: 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 the number of generations of a cyclic group having an order of 24

A: To find the number of generations of a cyclic group having an order of 24.

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: n point group D2d, for each of the irreducible representations, verify that the sum of the squares…

A: In point group D2d portions of the D2d character table D2d E 2S4 C2 2C2' 2□d A1 1 1 1 1 1 A2…

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

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Q: need help with cyclic groups plz, thanks

A: Given groups are,

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

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Q: Show that a group of order 77 is cyclic.

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