under the addition operation. a) Identify all subgroups of order 9. Explain how these groups are obtained. b) Construct a subgroup lattice diagram for H c) Give a group G that is isomorphic to H. Explain how to show that G  is isomorphic to H.

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Q: b. Find all abelian groups, up to isomorphism, of order 360.

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A: Yes , every subgroup of z is cyclic

Q: b. Find all abelian groups, up to isomorphism, of order 720.

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Q: Construct a subgroup lattice for the group Z/48Z.

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Q: Let Z denote the group of integers under addtion. Is every subgroup of Z cyclic? Why? Describe all…

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Q: prove that a group G of order p^2, where p is a prime, is abelian.

A: Suppose, G is a group of order p2 where p is prime.

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Q: Prove that every group of order 675 has a normal Sylow 5-subgroup.

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Q: Give a list, up to isomorphism, without repetition, of all abelian groups of order 72.

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