Help me!

[Camila Inethe]

12. Sejam r, s elementos de Q. Demonstre que a coleção dada por {mr + ns | m, n ∈ Z}
é um subgrupo cíclico do grupo aditivo Q.

 

[Deleted member 4993]

12. Sejam r, s elementos de Q. Demonstre que a coleção dada por {mr + ns | m, n ∈ Z}
é um subgrupo cíclico do grupo aditivo Q.

Please include a translation (english) so that maximum number of tutors can assist you.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Dr.Peterson]

12. Sejam r, s elementos de Q. Demonstre que a coleção dada por {mr + ns | m, n ∈ Z}
é um subgrupo cíclico do grupo aditivo Q.

Google says that this means

12. Let r be the elements of Q. Demonstrate that the collection given by {mr + ns | m, n ∈ Z} is a cyclic subgroup of the additive group Q.​

It seems to have lost "s", so I suppose it's really

12. Let r, s be elements of Q. Demonstrate that the collection given by {mr + ns | m, n ∈ Z} is a cyclic subgroup of the additive group Q.​

Now we need to know what help you need. Please show whatever you can do, starting with statements of the definitions needed, notably "cyclic subgroup". Can you show that this set is a subgroup? Can you find a generator for it?

If you have specific questions about the problem, please ask them.