Let P be a Sylow 19-subgroup and Q be a Sylow 7-subgroup. Then PQ is a subgroup of G of order: O 21 O 57 O None of the choices 8 O 133 O 399

Q: Let a be an element of order 8 in a group G. 6 Then order of a Select one: O a. 6 о Б.48 C. 2 d. 4

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Q: The index of [G:H] is a prime number that divides H and divides G O the double number of left or…

A: The double number of left or right cosets of H in G.

Q: Find all the conjugate subgroups of S3, which are conjugate to C2 .

A: Given-S3 To find- all the conjugate subgroup of S3 which are conjugate

Q: list the elements of the subgroup generated by the subset {18, 24, 39} of Z

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Q: Find the number of sylow 5 subgroups, sylow 7 subgroups and sylow 2 subgroups of A5

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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

A:

Q: Determine the number of Sylow 2-subgroups of D2m, where m is anodd integer at least 3.

A: For an integer m ≥ 3, the dihedral group D2m of order 2 m is D2m={a, b|am = b2 =1, b a=a-1 b }…

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

A: The explanation of the solution as follows:

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: Find four different subgroups of S4 that are isomorphic to S3.

A: If there exists an isomorphism between the subgroups they are called isomorphic ( Isomorphism is…

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

A: The solution is given as

Q: 2.5 what is/ I in Radians in toller Following Ama sonal are functions -2720 <212 1 2 noitonut tos a)…

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Q: Determine the number of Sylow 2-subgroups of D2m, where m is anodd integer at least 3.

A: As per the question we are given the dihedral group D2m and we have to find the number of total…

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: Determine the subgroup lattice for Zp. When p= any prime number.

A: Let H be a subgroup of group G, then H must divide GNow, ℤp=p, prime, the subgroups of ℤp are those…

Q: How many Sylow 3-subgroups of S5 are there? Exhibit five.

A: To find the Sylow 3-subgroup of S5.

Q: 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 =…

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

A: We are asked to find the subgroup of z24

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…