In the group Z, find а. (8, 14); b. (8, 13); с. (6, 15); d. (m, п); е. (12, 18, 45). In each part, find an integer k such that the subgroup is (k).

Q: 5-) Find all elements in his which has multiplcn the interse, then find their inverses

A: The objective of the question is determine the elements of Z15  and evaluate the   multiplicative…

Q: In the frieze group F7, write x-3zxyz in the form xnymz k.

A: It is known that F7=xnymzk∥n∈Z,m=0,k=0 or k=1 and x is the translation of R2, and it map u,v to…

Q: Find the order of the given elements in the factor groups. (a) 7+ (3) in Z15/(3). (b) (3, 1) + ((1,…

A: a) we need to find the order of the element 7+<3> in ℤ15/<3> Since,…

Q: 5. A group G has subgroups {a,b},{a,6, c, d, f } and {a,d}. The identity element of G is А. d В. с…

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Q: Consider from the b the Symmetric group. 1 2 3 5 6 7 7 5 4 1 2 36 3 5 6 = 3 7 15 a) Express each of…

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Q: 17. Compute d = ged(28, 124). Find integers x, y so that 28x + 124y = d. 18. Find the order of the…

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Q: (a) (Z4, +). (b) (Z5, .). (c) (Z5, +). (d) (Z4, .). (e) (Z6, .).

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Q: (b) Let H= ((3,3, 6)), the cyclic subgroup of G generated by (3,3,6). Determine |G/H.

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Q: Give the order of the element in the factor group (2,3)+⟨(0,3)⟩ in (Z10×Z4)/⟨(0,3)⟩

A: The order of the element (2 3 +  <(0, 3)> in (Z⁠⁠⁠⁠⁠⁠⁠10×Z4) / <(0, 3)> is…

Q: Find all subgroups of U(7)

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Q: Let G be group. Assume that Set H₁ = and H₂ =<b) Assume \ H₁|-21 and | H₂ | =10 a) Show that HinH₂…

A: If G be any group  and H1,H2 be two subgroups of G then we prove in general H1nH2 always a subgroup…

Q: What is the difference between a proper subgroup and a subgroup?

A: Here, we will tell the difference between a subgroup and a proper subgroup.Order of group means…

Q: In the frieze group F7, write x2yzxz in the form xnymz k.

A: It is given that, F7=xnymzk|n∈Z, m=0 or m=1, k=0 or k=1. we need to write x2yzxz  in the form of…

Q: 2. Let G = Z50 and consider it's subgroup H = (5). Find all coset representatives of 3+ H.

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

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Q: Find the order of the cyclic subgroup of 224 generated by 18. Find the order of 2/3 x 24. Find the…

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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: A group G has order 4n. where n is odd. Show that G has no subgroup of order 8.

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Q: def S ER a ca> Show thats is a subgroup ob (M2(R),+). (6) Show that ib A, B ES then ABES. (C) Find…

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Q: Find all the cosets of the subgroup 4Z of Z

A: In the group of integers under addition, the subgroup consists of all multiples of 4, i.e., .A coset…

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: Write out the Cayley table for the dihedral group D6 = {1,r,r2,s,sr,sr2}. (In general, we apply the…

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Q: 4. a) Let H be the set of elements [a b] of G of GL(2,R) such that ab- bc = 1. Show that H is a…

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Q: Find the decomposition of the representation Sym³V

A: The objective is to find the decomposition of the representation of Sym3V

Q: Consider the group D4 = (a, b) = {e = (1), a, a², a³, b, ab, a²b, a³b} %3D where a = (1 23 4) and b…

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Q: X={1,2,0,,8,3,5}. (a) Find all possible permutations and show that its form a group. (b) Find its…

A: Note: According to our guidelines We’ll answer the first 3 subparts of the question since the exact…

Q: 1.)Integrate: ∫(x+1)(x+2)^6dx Group of answer choices a.)(2/56) (7x + 6)(x + 2)7 + C b.)(2/56)…

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Q: Show that if a Sylow P subgroup is normal then it is characteristic

A: If a Sylow subgroup is normal, then it is the unique subgroup of that order, i.e. if P◃G

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

A: We have to find Sylow 5-subgroups of S_5

Q: The elements of the quotient group (2/8). 12 (0,1,2,3,...,8) 1- 2- -208,-108,008,108,208,...) 3- 4-…

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Q: {Ro,R180, D, V} {Ro,R180, D, D'} {Ro,R90, R180, R270} {Ro,R180; H, V}

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Q: The group U(14) has: اختر احدى الجابات only 2 subgroups 4 sub groups 7 subgroups 6 sub groups

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Q: Q1) Compute the value of representation √√√3-i in exponential representation and polar

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Q: a) Find a generating set of U(20) with two elements. b) Use the generators you found in part (a) and…

A: The set of integers modulo n defined by Un=k:gcdk,n=1 The set Un is a group under multiplication…

Q: Find the subgroup of Dn generated by r2 and r2s, distinguishing carefully between the cases n odd…

A: Subgroup generated by r2 and r^2s in Dn​: We will analyze the subgroup generated by r2 and r2s in…

Q: If G is a finite group with |G|<180 andG has subgroups of orders 10, 18 and 30 then the order of G…

A: Use the fact that order of subgroup divides order of group

Q: Suppose that a subgroup H of S5 contains a 5-cycle and a 2-cycle.Show that H = S5.

A: It is given that, H be a subgroup of S5 which contains a 5-cycle and a 2-cycle. We have to show…

Q: entire elements of D8 in terms of products of disjoint cycles in S8 ?

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