zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The Schur multiplier of a pair of groups. (English) Zbl 0948.20026

In this article the author develops the theory of a Schur multiplier for pairs of groups and he shows that it leads to a more systematic treatment of a number of results on the usual multiplier. In several instances this treatment yields sharper results.

The Schur multiplier of the pair (G,N), where N is a normal subgroup of G, is defined as a functorial Abelian group (G,N) whose principal feature is a natural exact sequence

H 3 (G,)H 3 (G/N,)(G,N)(G)(G/N)N/[N,G](G) ab (G/N) ab 0

((K)=(K,K)). The definition is given via classifying spaces of groups but a purely homological algebraic definition and proof of the exactness of the above sequence is also given by the author [in Glasg. Math. J. 29, 13-19 (1987; Zbl 0631.20040)].


MSC:
20J05Homological methods in group theory
19C09Central extensions and Schur multipliers
20E22Extensions, wreath products, and other compositions of groups