Group is a term used by different air forces for an element of military organization. The size of a group varies considerably between different countries. The terms group and wing are used differently in different air forces and this can cause confusion.
At the present time, groups control stations, although expeditionary air groups control expeditionary air wings directly. Groups are directly subordinate to a command (or, historically, to a tactical air force).
When the RAF was formed, an officer with the rank of Group Captain (equivalent to Colonel) commanded such a unit, although they have been commanded by Air Vice-Marshals since before the Second World War.
By contrast, in the French Armée de l'Air, a groupe may comprise only one squadron (escadron). Similarly, In the United States Air Force and the United States Marine Corps, a group is a formation consisting of as few as two squadrons. Two or more groups form a wing.
Therefore a British group is equivalent to a US wing, which is in turn equivalent to an army regiment, whereas one step down the nomenclature, a British wing is equivalent to a US group.