Q/ How many non-trivial subgroups in s3 a) 2 b) 3 c) 4 d) 5

Q: How many non-trivial subgroups in S3? 3 4 5

A: Trivial subgroup: A subgroup containing identity element is called as trivial subgroup and other…

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Q: De Morgan's law

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A: Given that M and N are two R-modules. We have to show that HomM,N is not a group under composition.…

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A: we need to give the example of open sets whose intersection is not open. Note: Intersection of…

Q: o:Z, →Z, A GROUP HOMOMORPHISM 30 30 KER () = {0,5,10,15, 20, 25} o(13) = 6 now THAT, 0" (6) FIND ?

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Q: How many subgroups of order 4 does D4 have?

A: Solution: Assume the following dihedral group D4, The above group consists of three subgroups of…

Q: 2. Determine whether the following multigraphs are Eulerian, semi-Eulerian or neither. Explain your…

A: Explanation we have to shown whether the given multigraphs are Eulerian , semi-Eulerian or neither…

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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…

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Q: In a group G,let a,b and ab have order 2.show that ab=ba

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Q: How many non-trivial subgroups in S3? O 2 O 4 5 3.

A: To find the number of non trivial subgroups of S3.

Q: 6. Show that if p is a prime number, then Z/pZ has no proper non-trivial subgroups.

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Q: Q/ How many non-trivial subgroups in s3 ? a) 2 b) 3 c) 4

A: We know that S3 = (1) , (1,2) , (1,3) , (2,3) , (1,2,3) , (1,2,3) Thus the subgroups of S3 are given…

Q: Suppose ACB and BCC. Show that = {A, B-A, C-B} is a partition of C.

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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: Show that Z has infinitely many subgroups isomorphic to Z.

A: We have to show that Z has an infinitely many subgroups isomorphic to Z.

Q: ] Let N be the subgroup of (Z15, +) generated by 3, that is N = . i- What is the order of N+ 2 in…

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Q: Show that S = SU(2) contains a subgroup isomorphic to S'.

A: Let's define S1 as the set { (x,y)∣ x2+y2 = 1 } ⊂ R2 we may think of S3 as S3={ (a,b) ∈ C2:…

Q: How many Sylow 5-subgroups of S5 are there? Exhibit two.

A: We have that |Sn| = n! Hence, |S5| = 5! = 120 = 23.32.5 By Third Sylow Theorem the number of Sylow-5…

Q: How many non-trivial subgroups in S3? 4 O 5

A: Given group is S3 S3=3!=6 In total, there are 6 elements in the group S3 Elements of the given group…

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

A: We know that τ(n) is number of positive divisors of n Also τpaqbrc = (a+1)(b+1)(c+1) , where p , q ,…

Q: is a subgroup of Z, of order 12 O 12 5, 3.

A: The explanation of the solution as follows:

Q: How many subgroups in Z/30Z 4 30 6 CO

A: Here we have group z/30z and find its number of subgroups.

Q: The set S=[1,3) is not compact. Which open cover of S contains a finite subcover?

A: This is the question of Topology.

Q: How many subgroups are there in Z/14Z?

A: Subgroup: Let (G, ∙) be a group and S be a non‐empty subset of G.Then, S is called a subgroup of G…

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

A: Answer : 1 right cancelation law

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.

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Q: Show by means of a membership table that both absorption laws are identities.

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Q: In the group U (I6) compute, (a) 5.7, and (b) 3

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Q: are rings. (Z,+,.), (R,t,.),(Q,+,.) a

A: (Z,+,.) , (R,+,.) , (Q,+,.) Are rings

Q: Let a,b,c be intergers with gcd(a,b)=1 and c|(a+b) (c divides a+b). Prove that gcd(a,c)=1 and…

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Q: Let A = {a,b, c} and B = {b, c, a}. Prove that A = B. Thus, the order %3| in which the elements are…

A: The given sets are A={a,b,c} and B={b,c,a}we have to show that A=BResult : two sets A and B are…

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Q: Suppose that a,beG such that a = m and b =n with Gcd (m,n) = 1. Then n | is in mn

A: Suppose that a, b∈G such that a=mb=n and Gcdm, n=1 i.e., m and n are relatively prime. We will find…

Q: In Z24 the number of all subgroups is 8 O 6.

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Q: How many subgroups are there in D4? Also find them.

A: D4 has 8 elements:. {1, r, r2, r3, d1, d2, b1, b2,}. where r is the rotation on 90◦, d1, d2 are…

Q: Let X be a non-empty set, Show that whether (P(X),n) is a group or not

A: given  Let x be a non empty set, Show that whether  (p(x),∩) is a group or not we need to show it is…