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- Whitehead's_lemma abstract "Whitehead's lemma is a technical result in abstract algebra used in algebraic K-theory. It states that a matrix of the form is equivalent to the identity matrix by elementary transformations (that is, transvections):Here, indicates a matrix whose diagonal block is and entry is .The name "Whitehead's lemma" also refers to the closely related result that the derived group of the stable general linear group is the group generated by elementary matrices. In symbols, .This holds for the stable group (the direct limit of matrices of finite size) over any ring, but not in general for the unstable groups, even over a field. For instance for one has:where Alt(3) and Sym(3) denote the alternating resp. symmetric group on 3 letters.".
- Whitehead's_lemma wikiPageID "4705059".
- Whitehead's_lemma wikiPageRevisionID "555668458".
- Whitehead's_lemma hasPhotoCollection Whitehead's_lemma.
- Whitehead's_lemma subject Category:K-theory.
- Whitehead's_lemma subject Category:Lemmas.
- Whitehead's_lemma subject Category:Matrix_theory.
- Whitehead's_lemma subject Category:Theorems_in_abstract_algebra.
- Whitehead's_lemma type Abstraction100002137.
- Whitehead's_lemma type Communication100033020.
- Whitehead's_lemma type Lemma106751833.
- Whitehead's_lemma type Lemmas.
- Whitehead's_lemma type Message106598915.
- Whitehead's_lemma type Proposition106750804.
- Whitehead's_lemma type Statement106722453.
- Whitehead's_lemma type Theorem106752293.
- Whitehead's_lemma type TheoremsInAbstractAlgebra.
- Whitehead's_lemma comment "Whitehead's lemma is a technical result in abstract algebra used in algebraic K-theory. It states that a matrix of the form is equivalent to the identity matrix by elementary transformations (that is, transvections):Here, indicates a matrix whose diagonal block is and entry is .The name "Whitehead's lemma" also refers to the closely related result that the derived group of the stable general linear group is the group generated by elementary matrices.".
- Whitehead's_lemma label "Lemma von Whitehead".
- Whitehead's_lemma label "Lemme de Whitehead".
- Whitehead's_lemma label "Whitehead's lemma".
- Whitehead's_lemma sameAs Lemma_von_Whitehead.
- Whitehead's_lemma sameAs Lemme_de_Whitehead.
- Whitehead's_lemma sameAs m.0cj871.
- Whitehead's_lemma sameAs Q1816970.
- Whitehead's_lemma sameAs Q1816970.
- Whitehead's_lemma sameAs Whitehead's_lemma.
- Whitehead's_lemma wasDerivedFrom Whitehead's_lemma?oldid=555668458.
- Whitehead's_lemma isPrimaryTopicOf Whitehead's_lemma.