Current theories imply text-based computer networks are socially barren, but computer-mediated interaction (CMI) research contradicts this. A cognitive perspective suggests individuals in groups construct cognitions regarding the task (purpose), other people (relationships), and the group (identity), and these drive the interaction. Three core psychological process follow: resolving task information, relating to others and representing the group. This gives three types of influence: informational, personal and normative, and three group purposes: task resolution, interpersonal relationships and group unity. Group unity occurs when group members represent a common identity. The traditional communication threads of message content and sender context therefore require a third - behavioural position. Many-to-many exchange of member positions allows the group position to be transmitted to the group. A picture emerges of three parallel processes overlapping in behaviour, although CMI allows them to be isolated and investigated. This model extends most theories of computer-mediated group interaction. It implies there is no “best” type of group interaction support, because there is no best process. The groupware challenge is to offer the flexibility to support all three processes in combination.