Outwest, I believe, could be mistaken, that in the optical engineer dialect of English a lens element is a single piece of glass. A group is one or more elements (if more than one, all cemented into one piece with no internal air spaces) with air on both sides. Lenses are sometimes mounted up in barrel or in shutter with one or more groups on one (or both) sides of a diaphragm. When the groups on one side of the diaphragm are mounted so that they can be removed as a unit -- this isn't the case for all lenses, when my friend Charlie Barringer unscrewed what he thought was a 55/5.6 Lamegon's rear cell from its shutter, the groups fell out -- the unit is called a cell.
A four element double Gauss type's lenses are laid out this way: ((|)) where ( is a single element and | is the diaphragm.
The OP doesn't need to know about Perigraphes. Short story, Perigraphe is a Berthiot trade name that was applied to two quite different dagor type (six elements in two groups) lenses. f/6.8, not particularly wide angle (late ones, 65 degrees), and f/14, extreme wide angle (late ones, 100 degrees). I don't recall seeing either in shutter, but the f/6.8ers can be adapted. The gap between f/14ers' cells, especially the shorter focal lengths, is said to be too narrow for them to be put in shutter. Could be, but the cells' mounting -- they're in quite wide symmetrical dished plates -- is another obstacle to putting them in shutter.