Group fares
There are 3 main types of group fares within Scotland. Scotrail offers a group ticket for 3 or more people travelling together, for a third off on the following routes: Edinburgh/Glasgow via Falkirk High, Falkirk Grahamston, Airdrie, Shotts, and Carstairs. Edinburgh or Glasgow to Dunblane, Stirling and Alloa. These tickets are valid in the off peak hours - anytime at the weekend, and weekdays from 0915 until 1641, then from 1816 until last service. Valid on Scotrail services, and also LNER's (London North Eastern Railway) Dunbar - Edinburgh - Motherwell/Glasgow/Falkirk/Stirling limited services. No need to book in advance. These can be bought at ticket offices only (onboard if the ticket office is closed), and can't be bought from Ticket Vending Machines. Break of Journey is not permitted on these tickets - they are point to point only. If 4 of you are travelling out, but only 2 are returning - that is fine, but no refunds for the 2 not returning. Only one ticket is issued per direction for the group.
London North Eastern Railway (LNER) offers group fares on their limited services from Edinburgh to Inverness and Aberdeen and most intermediate stations in standard class and first class. They are offered on their advance purchase/fixed fares only, so make sure you want the times you book, 25% off the regular advance fare if booked at their website, or 20% off if using any ticket office, or the special "group advance" button on the "railcard" drop down menu on their red and grey Ticket Vending Machines at Edinburgh or Aberdeen stations .
Scotrail offers "friends and family" fares for groups of 3 or 4 people travelling together, on the Edinburgh or Glasgow to Aviemore/Inverness/Arbroath/Montrose/Stonehaven/Aberdeen services. There is very limited seat availability for these, especially on Fridays and Sundays, and during the prime summer months. They can work out to be less than £8 per person per direction. They are fixed tickets, and not changeable after purchased - so select carefully. All must travel together.