**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: *H*_{1}(*G*, **Z**) = *H*_{2}(*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.

Read more about Superperfect Group: Definition, Examples

### Other articles related to "superperfect group, group, superperfect":

**Superperfect Group**- Examples

... For example, if G is the fundamental

**group**of a homology sphere, then G is

**superperfect**... The smallest finite, non-trivial

**superperfect group**is the binary icosahedral

**group**(the fundamental

**group**of the PoincarĂ© homology sphere) ... The alternating

**group**A5 is perfect but not

**superperfect**it has a non-trivial central extension, the binary icosahedral

**group**(which is in fact its UCE, and is

**superperfect**) ...

### Famous quotes containing the word group:

“It is not God that is worshipped but the *group* or authority that claims to speak in His name. Sin becomes disobedience to authority not violation of integrity.”

—Sarvepalli, Sir Radhakrishnan (1888–1975)

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