Let H be a subgroup of G and let a, be G. If Ha Hb, then* %3D aH = bH O a-1H = b-1H O Ha = Hb Ha-1 = Hb1 %3D Ha-1 = Hb-1 O None of the choices

Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -5 + 2Z contains the…

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Q: Let M be a subgroup of group G, and a,b e G, then aM=bM→ a-1 b € M True O False O

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Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -3 + 2Z contains the…

A: Given that 2Z is the set of all even integers.

Q: 3) Prove that if A and B are subsets of G with A C B then Cc(B) is a subgroup of CG(A).

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Q: 10. Let A be a subgroup of G, and let B be a subgroup of H. Show that A×B is a subgroup of G×

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Q: Let G = U(15) and H ={1,14} be a subgroup of G. The distinct left cosets of H in G are: * None of…

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Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -5 + 2Z contains the…

A: Given: 2Z is a subgroup of (Z,+). We have to find the right coset of -5+2Z.

Q: by LetG = {(ª : a, b, , c, d e Z under addition let H EG : a +b + c + d = 1 € Z} H is a %3D subgroup…

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Q: Let A and B be subgroups of G such that AB = BA. Then AB is a subgroup of G.. Select one: True False

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Q: Let H be a subgroup of G. If a and b are elements of G such that aH = bH, then Ja| = |b|. %3D

A: Given that Let H be a subgroup  of G. If a and b are elements of G such that aH = bH, then a=b. To…

Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -5 + 2Z contains the…

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Q: is a subgroup of Z1, of order: 3 12 O 1 The following is a Cayley table for a group G. 2. 3.4 = 2 3…

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Q: Determine which of the following is a normal subgroup SL(2, R) Z, None of them S3 GL(2, R)

A: Zn is not a sub-group but the subgroups of Zn are normal subgroups.

Q: Let G, and G, be two groups. Let H and H, be normal subgroups of G G, respectively then @ H, x H, 4G…

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Q: Let H be a subgroup of G and let a, b E G. If aH = bH, then * На 1 — НЬ 1 О На %3Dнь На-1 %3D НЬ-1…

A: H is a subgroup of G and a,b belongs to G. If aH=bH then a and b lies in the same left coset of H.…

Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -5 + 2Z contains the…

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Q: prove That :- let H and K be subgroups of agroupG of the m is ormal a HK is subgroup of G →1f one

A: Subgroup of a group G

Q: 4. If H is a subgroup of G, then show that the set W = ngHg¹ is a normal 9€G subgroup of G.

A: Given That : H is a subgroup of G  To Show: The set W=∩g∈GgHg-1 is a normal Subgroup.

Q: Let H be a subgroup of a group G and a, b EG. Then b E aH if and only if O None of these O ab EH О…

A: The solution is :

Q: If H and K are subgroups of G, IH|= 20 and |K|=32 then a possible value of |HNK| is O 2 O 8 O 16

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Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -5 + 2Z contains the…

A: 2Z ={ .........  , -8, -6 , -4 , -2 , 0 , 2, 4, 6 , 8, ....}

Q: If H and K are subgroups of G, |H|= 16 and |K|=28 then a possible value of |HNK| is * 4 O 16

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Q: Let H be a subgroup of a group G and a, b € G. Then b E aH if and only it O None of these O ab e H O…

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Q: If H and K are subgroups of G, |H|= 16 and |K|=28 then a possible value of |HNK| is * O 6 16 8. 4

A: Order of an subgroup should divide order of an group. Intersection of two subgroups again a…

Q: If H and K are subgroups of G, |H|= 18 and |K|=30 then a possible value of |HNK| is * 18 8 6. 4

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Q: Q7. Suppose that the index of the subgroup H in G is two. If a and b are not in H, then ab ∈ H.…

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Q: The set of all even integers 2Z is a subgroup of (Z, +) Then the right coset -5 + 2Z contains the…

A: Suppose G is a group and H is a subgroup of G .Then set a+H is left coset if H in G . set H+a is…

Q: Let H be a subgroup of a group G and a, bEG. Then bE aH if and only if * O None of these O ab e H O…

A: here option (c) is true.

Q: If H and K are subgroups of G, |H|= 16 and |K|=28 then a possible value of |HNK| is * 8. O 16 4 O 6

A: Since you have posted multiple questions only the first question will be answered. It is given that…

Q: If H and K are subgroups of G, |H]= 18 and |K|=30 then a possible value of |HNK| is * O 8 6. 4 O 18

A: For complete solution kindly see the below steps.

Q: One of the following is a p-sylow subgroup of the group Z, × Zg H={(0,0),(0,4)} O…

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Q: The set A := {(1), (1 2 3), (2 3 4)} forms a subgroup of the permutation group (G,.). O True O False

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Q: If H and K are subgroups of G, |H|= 16 and IK|=28 then a possible value of |HNK| is * O 16 4 8.

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Q: a b с d e f a b c d e f cdf a b e d e f a ecdb a b fc a b c d e f b f Answer: deca ecbfad Enter a…

A: We have to solve given problem:

Q: If H and K are subgroups of G, |H|= 16 and |K|=28 then a possible value of |HNK| is 8 O 16 4 6

A: Answer is 4.

Q: Let G Są and let K = {1,(1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}. K is a normal subgroup of G. What is…

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Q: Let H and K be two subgroups of a group G. Let HK={ab|a∈H,b∈K}. Then HK is a subgroup of G. true or…

A: F hv

Q: Let H be a subgroup of G. Show that if aH Deduce that H is normal in G if and only if every left…

A: Let's first show abH⊆Hab Let,  abh=abh=ah1,b Since Hb=bHfor some h1∈H Therefore,  abh=ah1b  Since,…

Q: If H and K are subgroups of G, |H|= 16 and IK|=28 then a possible value of |HNK| is * O 16 6. 4 O O…

A: H and K are subgroups of G H=16 and K=28 we have to find the possible value of H∩K

Q: Let G = {a° = e, a', a?, a', a*, a", a°, a?} and let H = (a²) be %3D %3D a cyclic subgroup of G find…

A: From given group it is clear that a is generator of group and group is cyclic

Q: Determine which of the following is a normal subgroup O GL(2. R) SL(2. R) O None of them Os. S,

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Q: Let H be a subgroup of G. If G has exactly one subgroup of order |H|, then show that for all g e G,…

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Q: Let H be a subgroup of G. Show that if aH = Deduce that H is normal in G if and only if every left…

A: Given:- Let H be a subgroup of G. To prove:- If aH=Hb for some a,b ∈G then aH=Ha. also if H is…

Q: Exercises: 1) Let G = (Z6,O) .Show which of the following subsets of G is a subgroup of it? a) H =…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: If H and K are subgroups of G, |H|= 20 and |K]=32 then a possible value of IHNKI is O 2 16

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Q: If H and K are subgroups of G, H|= 16 and |K|=28 then a possible value of |HNK| is * 4 О 16 6 00 ООО…

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Q: Let G = U(16) and H = {1, 9} be a subgroup of G. The distinct left cosets of H in G are: * О н, ЗН,…

A: As per our guideline we supposed to answer only first question , kindly repost other as next…

Q: to be the subset Let H be a subgroup of G. Define the normalizer of H in NG(H) = {g e G| gHg H}. (i)…

A: Let H be a subgroup of G. The normalizer of H in G is given by NGH= g∈G  gHg-1=H  A nonempty subset…

Q: Let H be a subgroup of a group G and a, bEG. ThenbE aH if and only if * O None of these O ab EH O…

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Q: A Let (A, +,.) be a subgroup of (M₂ (Z), +,.), Then A is ideal of M₂ (Z), where = {(ab) a, b, c €…

A: Let I be a non-empty subset of a ring (R,+,·). Then I is an ideal of (R,+,·) if and only if the…