Why can't I invite players to my faction?

Hit the Faction tab at the bottom right corner, then hit Mange Faction tab, then hit Invitations and from there you can either hit the Public Invite tab in the top right corner to put out a Faction recruitment message in the city chat or you can manually one by one invite the list of available players that you'll seeblisted when you hit Invitations. If you do the latter, go back and then immediately hit Invitations again and it will give you a new list of players to invite, because there isn't enough room for all of them the first time you hit Invitations. So hit Invitations, then one by one invite players, press Back, hit Invitations again, and the one by one invite the refreshed list that it will provide you. Repeat this process until there are no more players listed after you hit Invite. Also, the price for Public Invite is 20 gold for the first time. It will subsequently rise each time you want to do it again in the same day. At the end of the day it will return to 20 gold again.

Only R5 and R4s can invite new members. You may not have permission to manage the faction.

Another reason maybe because your city is new, your friends can't relocate to the city based on their start date. New cities go through an immigration process to keep long time players out of new cities to give that city and its newer players a chance to grow and not be over run by advanced players.