Are plastic bottle caps able to be recycled with the bottles?

I had heard a while ago that they weren't, so I have been throwing them away as I didn't want ALL the recycling to be unusable (I recycle everything), but I just wanted to double check that as it didn't seem right to me.
Update: I do take my recycling to the center, it isn't picked up from my apartment. So best thing to do is leave the bottles in the recycling bag with the plastic, glass, and cardboard (my center DOES allow it all to be together) because it will all be sorted anyway?
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