High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, in the realm of group theory, a group is said to be superperfect when its first two homology groups are trivial: H_1(G;mathbf{Z})=H_2(G;mathbf{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.

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