Bantari wrote:So 'a live group' and 'alive group' are two different things?
It depends on accepted presuppositions. E.g., in strict rules English, if I work with the Japanese 2003 Rules, then "alive" is defined and so may be used while "live" is undefined and may not be used. (One could define though: "Live is alive. Life is alive. Living is alive.")
E.g., in ordinary English, presuppositions are different. There all grammatical forms of a word (in a particular meaning - not in an entirely different meaning) are already assumed to have (about) the same meaning as one particular representative grammatical form.
Things become complicated when ordinary English is used in all its variation power with different meanings for the same word, see the World Amateur Go Championship Rules with their many very different meanings of "surrounded" etc.
Lawyers like nouns so much because they have an only restricted grammatical variation. Careful rules writers or mathematicians like defined terms so much because they (almost) do not have any variation.