There were some gloves on the floor, so I picked them up and put them on the table.
Could you explain why it's necessary to repeat "them" after "and"? Is it not clear the object after "and"? I think the sentence would be easier to read if we could write "... so I picked them up and put on the table."
I can't say like that, right? In my native language it's possible and often we don't repeat "them" after "and".