Superperfect Group

Superperfect Group

In mathematics, in the realm of group theory, a group is said to be superperfect when its first two homology groups are trivial: H₁(G, Z) = H₂(G, Z) = 0. This is stronger than a perfect group, which is one whose first homology group vanishes. In more classical terms, a superperfect group is one whose abelianization and Schur multiplier both vanish; abelianization equals the first homology, while the Schur multiplier equals the second homology.