Let G be a cyclic group of order 135. The number of generators of G is The number of elements of Dihedral group D11 is How many elements of a cyclic group with order 20 have order dividing 5? How many elements of a cyclic group with order 15 have order 5? What is the order of Z13?

Q: for each of the group Z2,Z4,Z6 INDICATE WHICH CYCLIC. FOR those cyclic list  all the generators?

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Q: Find the order of each of the following elements in the multiplicative group of units Up. a. [2] for…

A: Consider the multiplicative group U13. Find the order of element 2.   The identity of a…

Q: How many nonisomorphic frieze groups are there?

A: To find- The number of non isomorphic frieze groups.

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

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Q: Which of the following is cyclic group? О а. Q O b. C О с. Z O d. R е. N

A: definition: a group G is said to be cyclic if G=<g> for some g∈G. g is a generator of…

Q: . Consider the group (Z30, +). (a) Find the orders of the elements 3, 5, 6, 7,8, 18, 19, 24 and 25.…

A: The order of an element is n , when n is the least such that, n.a=0 3.10 = 0 and 19 the least , so…

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

A: Abstract Algebra, Dihedral group

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

A: using  third Sylow Theorem

Q: What is the order of the (entire) symmetry group in R3of a 3-prism?

A: A 3-prism is a polyhedron with two congruent and parallel faces (called the bases) and rectangular…

Q: what will be the class equation of a group of order 12? In general what steps do we follow to find…

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Q: Find the number of non-isomorphic abelian groups of order 160. How many of these groups will be…

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Q: How many elements of order 33 are there in the dihedral group 33 ?D

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: Let G = <a, b | a6 = b3 = e, b-1ab = a3>. How many elements doesG have? To what familiar group…

A: Given set is G = <a, b | a^6 = b^3 = e, b^-1ab = a^3>.

Q: Question: Find the order of every element in the symmetry group of D4. I know the order each group…

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Q: Let G = <a, b | a6 = b3 = e, b-1ab = a3>. How many elements doesG have? To what familiar group…

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Q: ic group, order of a group/element 1. Write a definition of a cyclic group. Provide two examples of…

A: We have to write the definition of cyclic group.

Q: Depine Dihedral group of order 8. Write two non-trival Subgroups of Dihedral group

A: Dihedral group of order 8 is given by     D4 = group of symmetries of a square          = {R0, R90,…

Q: 1. Show that every group of prime order is simple.

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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: Q 3 Find the total number of binary operations on a set containing 100 ele- ments. Q 4 Give an…

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Q: 4*. Let a and b be elements of orders 5 and 8 in a group of order 120. List the possible orders of…

A: To list the possible orders of the subgroup generated by a and b under the given conditions

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

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Q: The alternating group A5 has 5 conjugacy classes, of sizes 1, 12, 12, 15, 20. Use this information…

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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: (1).* 4 and |6| = 2, Let G be a group. Let a, b EG such that |a| and a b = ba. Then determine |ba|,…

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Q: 1. Let p be a prime number. Find the number of generators of the cyclic group Z where r is an…

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Q: (S) Is all groups of ve, glve aIl pie. about groups of order 5? (Are they always commutative).

A: Concept:

Q: Alte

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Q: How much cyclic groups does have U(15

A: Cyclic group  is a group that is generated by a single element.

Q: for each of the group Z2,Z3,Z4,Z10 indicate which are cyclic. for those that are cyclic list all the…

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Q: find the number of elements in the indicated cyclic group. the cyclic subgroup of Z30 generated by…

A: To find the number of elements in the cyclic subgroup  generated by 25, you need to determine all…

Q: 6.2 Which of the following groups are cyclic? a) Z12×Z, b) Z10x Zgs c) Z4xZ2sx Z, d) Z22XZ21 xZ6s

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Q: Show if the shown group is cyclic or not. If cyclic, provide its generator/s for H H = ({a +bv2 : a,…

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

A: Cayley table for a group G is given as, The objective is to find 2*5*4 Since, G is a group. Hence,…

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

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Q: Ex. 29 Give the Cayley table for the group Zi2 under multiplication modulo 12.

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