Suppose G is a group. The Schur multiplier of G, denoted M(G), which ... * Perfect implies natural mapping from tensor square to exterior square ... ...
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#REDIRECT Schur multiplier of abelian group is its exterior square ... ...
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Suppose G is an abelian group. The Schur multiplier of G, denoted ... | arbitrary group instead of abelian group || Schur multiplier is ... ...
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Suppose G is a (not necessarily abelian) group. The tensor square ... Explicitly, it is the quotient of the free group on all formal symbols ... ...
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#redirect second homology group of abelian group is its exterior square ... ...
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The notion of Schur multiplier of a Lie ring is defined analogously ... | 1 || second homology group || It is the second defining ingredient::homology ... ...
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up to isomorphism, for a Lie ring of prime-square order p^2: # Abelian Lie ring whose additive group is cyclic group of prime-square ... ...
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Suppose G is the free nilpotent group of class c \ge 1 on a generating ... Then, the Schur multiplier M(G) = H_2(G;\mathbb{Z}) of G is the group ... ...
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A group G is termed epabelian if it satisfies the following equivalent ... # For any group K with a central subgroup H such that the quotient ... ...
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The exterior square of a group G (sometimes also called the non-abelian ... this coincides with the exterior square of abelian group. ... ...
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Suppose \pi is a set of primes. Suppose G is the free \pi-powered nilpotent group of class c \ge 1 ... ...
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The goal of this page is to discuss the second cohomology group for ... ==Computation of the group==
We use the formula for second cohomology ... ...
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Suppose G is an abelian group and A is an abelian group. Then, the ... Since G is also an abelian group, we have G^{\operatorname{ab}} = ... ...
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perfect group|Schur-trivial group
==Definition==
===Equivalent definitions ... * The trivial group is superperfect.
===Groups satisfying the property=== ... ...
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The Schur multiplier of a group G, denoted M(G), is an abelian group ... ===Equivalence of definitions===
* The equivalence of definitions ... ...
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Let G be a group isomorphic to the quotient group F/R, where F is ... In other words, it equals the quotient of the intersection of R with ... ...
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Suppose G is an abelian group and c is a positive integer. Denote ... M^{(c)}(G) \cong (c+1)^{th} \mbox{ graded component of } \mathcal{L}(G) ... ...
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{{group property implication|
stronger = FZ-group| weaker = group with finite derived subgroup}}
This result was proved ... ...
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The goal of this page is to discuss the second cohomology group for ... ==Computation of the group==
We use the formula for second cohomology ... ...
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precise center, or precise centre) of a group G, sometimes denoted ... extensions E with quotient group G, of the images in the group ... ...
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