Hello @LyndaElaine,
In Canvas there is not a way to differentiate assignments by groups. Depending on the settings in your instance, you can go to Settings --> Sections and group the students into different sections. When in the Assign To area of an assignment, you will then be able to select specific sections. You will need a different assignment per section to differentiate the material.
Alternatively, you could have all of the material for each group all in the same assignment and then just clearly communicate to them which material they should be using based on their groups.
Would either of those work for you?
--James