Group
A group is a set of pieces owned by the same player that are virtually connected. This means that the pieces can only be disconnected from each other if the player allows it.
A group typically relies on certain cells being empty. When the opponent plays in one of those cells, it is called an intrusion. An intrusion means that the owner of the group must play another move if he wants to restore the connection between his pieces.
A cell in which the opponent can intrude is called an intrusion point.
Chains and templates are examples of groups. More generally, a group typically consists of one or more chains connected by templates and double threats.
The "group" terminology is often used to say things like "Red's central group is connected to the upper edge", or "Blue's two groups are not yet connected to each other".