All modern broadband routers have wireless as per BIgpaw above. To join such routers there are a varietry of security hurdles. Some routers you have to push a button and then enter a 25 digit code, others have a straight password. It seems as though your Galaxy may have been linked in the past so that it can use the router.
You do not say where you are or what ISP you have, but there is a growing trend here in France for ALL routers (in private houses et(rc) to become universal hotspots to the clients of that ISP. IT may be that this method (which works well and extends the use geographically a lot) may develop where you are.
M
mjdodd
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