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Is it worth having a page for this term? I've found that the group concept helps me conceptualize certain rules more easily. While it doesn't make any previously impossible rules possible, it does make some rules easier. Consider one from the Origins tourney a couple years back: "AKHTBNI it contains exactly one piece that isn't touching another piece." Having the group concept in my arsenal made the rule fairly straightforward: "AKHTBNI it has exactly one one-piece group."

Is "AKHTBNI it has exactly one THREE-piece group," expressible with just plain touching terminology? Yes, but it's a bear. Try it.