Can I assign courses to groups of users?

Unfortunately, it is not yet possible to do this. Our tech team are working on bringing this feature to the app and we hope to have this live soon.

You are able to track if group members have taken a course in the Training Manager.
You may also find it helpful to use the Bulletins feature to send a message to a particular group. Use the content of the bulletin to request that they go into the training area to complete a specific course (or courses). This way you can also track that the recipient has received and read the bulletin request.