Find all inclusion between subgroups in Z/48Z

Q: Does Sn have a subgroup isomorphic to An other than An (n ≥ 5).

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Q: Give the lattice of subgroups of (Z2,), of (S,,0), and of (Z(20) ,)

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

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Q: Determine the subgroup lattice for Zp where p is any prime number

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Q: Is {0, 2, 4, 6} a subgroup of Zg? Justify your answer.

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Q: Prove or give counter example Every characteristic subgroup is fully invariant

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Q: Show that no proper subgroup of S4 contains both (1,2,3, 4) and (1,2).

A: We have to show that no proper subgroup of S4 contains both 1,2,3,4 and 1,2. We know that the…

Q: 12. Find all subgroups of Z2×Z4.

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

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Q: 2 Prove That D₂ = 8 cannot be the internal direct product of two of its proper subgroups.

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Q: 4 a

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Q: Find five subgroups of S5 of order 24.

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Q: If H and K are two subgroups of finite indices in G, then show that H ∩ K is also of finite index in…

A: If H and K are two subgroups of finite indices in G, then show that H ∩ K isalso of finite index in…

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: 8. Prove that Q is not a subcartesian product of infinite cyclic groups.

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Q: The set of all odd permutation subgroups in S, form

A: False,

Q: At now how many elements can be contained in a cyclic subgroup of ?A

A: There will be exactly 9 elements in a cyclic subgroup of order 9.

Q: Are there any other subgroups of order 3 & 2 ? For his vere'll consider all subsets of 3 and 2…

A: We see that S3 is a group of six elements. f is the element in S of order 3. Hence, <f>, <f…

Q: Find two p-groups of order 4 that are not isomorphic.

A: Consider the groups ℤ4  and  ℤ2⊕ℤ2. Clearly, both of the above groups are p-groups of order 4.

Q: In Z, find all generators of the subgroup <m> <n>.

A: The objective of the question is to find all generators of the subgroup <m> <n> in the…

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

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

Q: a) Clearly state all the subgroups of the additive group Explain why/how you have found all the…

A: We have to write subgroup of z_9.

Q: Find the subgroup of ℤ generated by the subset {6,9}.

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