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In mathematics, in the realm of group theo … 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.hur multiplier equals the second homology.
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| rdfs:comment |
In mathematics, in the realm of group theo … 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.hur multiplier equals the second homology.
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| rdfs:label |
Superperfect group
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