Nilpotent groups of a given class and solvablee solvable groups of a given class form varieties, each of these varieties is defined by commutator identities. Supersolvable groups of any class do not form a variety of groups. Moreover it is not a union of varieties because there exist exists a supersolvable group which generates a variety where not all groups are supersolvable. So there is no definition in terms of identities - commutator or not.
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Nilpotent groups of a given class and solvablee groups of a given class form varieties, each of these varieties is defined by commutator identities. Supersolvable groups of any class do not form a variety of groups. Moreover it is not a union of varieties because there exist a supersolvable group which generates a variety where not all groups are supersolvable. So there is no definition in terms of identities - commutator or not. |
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