Is "pirsumei nissa" incidental (a "byproduct") caused by the lighting of the Chanukah candles or is it a separate mitzvah?
I ask this, because, the mitzvah of lighting candles is only in one's home. One does not gain the mitzvah by lighting the candles in the office or the town square. So, if publicizing the miracle is a byproduct, it seems that this would be accomplished only when lighting at home.
If, however, it is a separate mitzvah, then wouldn't lighting the menorah in the town square or office accomplish this? Or do these lightings accomplish absolutely nothing other than to get people together to celebrate and enjoy a menorah lighting?
NOTE: I think Kitzur Shulchan Aruch (could be wrong about exact source) states that the lighting in the shul is for pirsumei nissah. So, perhaps, there is a mitzvah on its own, or is that a special thing unique to shul lighting?