How many subgroups of a not abelian group of order 6 is non-cyclic? Select one:

Q: How many subgroups of are equal to the subgroup ?

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Q: Give all the possible elementary divisors of a group of order 40.

A: 40=23×5 So, the possible elementary divisors of the group are 2,2,2,5,2,4,5 and 8,5

Q: Every subgroups of cyclic group is Select one: a. cyclic and normal b. not cyclic and normal C.…

A: Since you have asked multiple questions in single request.so we will answering only first question.…

Q: 4. Give an example of a pair of dihedral groups that have the same number of conjugacy classes as…

A: We know that Dihedral group is denoted by Dn. Its order is 2n. Here, to find the pairs of Dihedral…

Q: 6. Give an example of two groups with 9 elements each which are not isomorphic to each other (and…

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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: Which among is a non-cyclic group whose all proper subgroups are cyclic? U(12), Z8 , Z, U(10)?

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Q: Find cyclic subgroups of S4 that have three different orders.

A: There are more subgroups than just the cyclic ones.   Trivial:  there is <e> = {e}.   There…

Q: give an example of a finite, non-cyclic abelian group containing a container of order 5

A: Take the abelian group G=Z5×Z5 of order 25 whose every element (except identity) is of order 5 and…

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

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Q: Show that if n > 6, then the symmetric group Sn contains an element of order greater than n

A: According to the problem, we have

Q: Every cyclic group or order n is isomorphic to (Zn, +n) and every infinite cycle group is isomorphic…

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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: 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: b. Find all abelian groups, up to isomorphism, of order 360.

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Q: many

A: We have to find the number of generator of the given group of order

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

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Q: 1.Show that the set {5,10,25,35} is a group under multiplication modulo 40 by constructing its…

A: Let us denote the operation given in the question, multiplication modulo 40, with · and the usual…

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

A: using  third Sylow Theorem

Q: 4. List all of the abelian groups of order 24 (up to isomorphism).

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Q: Find all the subgroups of Z48. Then draw its lattice of subgroups diagram.

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

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

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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: The operation of composing any two symmetries in a dihedral group is commutative.

A: To find: The given statement true or false. The given statement: "The operation of composing any two…

Q: Give a list of all groups of order 8 and show why they are not isomorphic. for this you can show…

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Q: 5. How many automorphisms does Klein's 4-group have?

A: No of automorphism of Klein's 4-group:  K4={e,a,b,c} f1=eabceabc = I f2=eabceacb = bc f3=eabcecba =…

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: How many Abelian groups are there of size , up to isomorphism?325-72

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

Q: {a3 }, {a2 }, {a5 }, {a4 }   Which among is not a subgroup of a cyclic group of order 12?

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Q: A cyclic group is abelian

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Q: List six examples of non-Abelian groups of order 24.

A: The Oder is 24

Q: What is the smallest positive integer n such that there are two nonisomorphicgroups of order n? Name…

A: Non-isomorphic groups: Groups that have different Sylow-2 groups are non-isomorphic groups.

Q: Given two examples of finite abelian groups

A: Require examples of finite abelian groups.

Q: The identity element in a subgroup H of a group G must be the same as the identity element in G…

A: The identity element in a subgroup H of a group G must be the same as the identity element in G.

Q: Show that group Un (n th unit root) and group Zn are isomorphic.

A: There are n elements in the group (Zn,+). There are n elements in the group (Un,×). There are (n!/2)…

Q: Find the number of elements in the indicated cyclic group. The cyclic subgroup of z225 generated by…

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Q: List all abelian groups (up to isomorphism) of order 600

A: To List all abelian groups (up to isomorphism) of order 600

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: Find an example of a noncyclic group, all of whose proper subgroupsare cyclic.

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Q: Find the number of distinct regular tetrahedral dice that can be made by coloring its faces with…

A: The fundamental theorem of finite Abelian groups - " a finite Abelian group is isomorphic to a…

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: Give the Cayley table for the group Z2 under multiplication modulo 12.

A: Since , We know that Z12 = 0,1,2,3,4,5,6,7,8,9,10,11 and…

Q: 6.7 Construct a nonabelian group of order 16, and one of order 24.

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Q: 2) Given example of an infinite group in which every nontrivial subgroup is infinite.

A: Let G=a be an infinite cyclic group generated by a, whose identity element is e. Let g∈G, g≠e,…

Q: 5. Let a be an element of order n in a group and let k be a positive integer. Then =< a™dlnA)

A: To prove : ak=agcd(n,k) Let set d = gcd(n,k)  and then write k=dr by definition of gcd, We prove…

Q: Consider the alternating group A4. Identify the groups N and A4 /N up to an isomorphism.

A: Consider the alternating group A4. We need to Identify the groups N and A4 /N up to an isomorphism.…

Q: Let G = Zp × Zp. Is this group cyclic? As you know any cyclic group can be generated by one element.…

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