Is a subgroup of a product of two groups necessarily a product of two subgroups ? [on hold]

Is a subgroup of a product of two groups necessarily a product of two subgroups ?
Thanks !

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1 Answer
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Not necessarily, Consider the subgroup of Z×Z\mathbb Z\times \mathbb Z generated by (1,1)(1,1)

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This is the product of Z\mathbb Z with {1}\{1\}.
– Myridium
2 days ago

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@Myridium what substance are you on?
– Jorge Fernández Hidalgo
2 days ago

  

 

Am I making a dumb mistake? The way I interpret the OP’s question is such that in this case, they are looking for a direct product of subgroups of Z\mathbb Z isomorphic to the subgroup of Z×Z\mathbb Z \times \mathbb Z generated by (1,1)(1,1) (which is Z\mathbb Z).
– Myridium
2 days ago

  

 

Oh ok, I guess that makes sense. I’ll try to come up with something under that interpretation.
– Jorge Fernández Hidalgo
2 days ago

  

 

What about this subgroup of Z² : {(x, x) / x in Z} ?
– Zakaria Oussaad
2 days ago