Results 161 to 170 of about 75,652 (194)
Some of the next articles are maybe not open access.
1971
In this chapter we shall apply the theory of derived functors to the important special case where the ground ring Λ is the group ring ℤ G of an abstract group G over the integers. This will lead us to a definition of cohomology groups H n (G, A) and homology groups H n (G, B), n ≧ 0, where A is a left and B a right G-module (we speak of “G-modules ...
Peter J. Hilton, Urs Stammbach
openaire +1 more source
In this chapter we shall apply the theory of derived functors to the important special case where the ground ring Λ is the group ring ℤ G of an abstract group G over the integers. This will lead us to a definition of cohomology groups H n (G, A) and homology groups H n (G, B), n ≧ 0, where A is a left and B a right G-module (we speak of “G-modules ...
Peter J. Hilton, Urs Stammbach
openaire +1 more source
Invariants and Cohomology of Groups
2004Given an extension of finite groups \(1\to H\to G @>\pi>> K\to 1\) and a prime \(p\) dividing the order of \(G\), let \(|A_p(K)|\) denote the geometric realization of the poset of elementary abelian \(p\)-subgroups of \(K\) and, for any \(i\)-simplex \(\sigma_i\), denote its stabilizer by \(K_{\sigma_i}\) and its orbit representative by \([\sigma_i]\).
Adem, Alejandro, Milgram, R. James
openaire +2 more sources
2019
AbstractThis chapter introduces the basic ingredients of the cohomology of groups and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: integral homology of finite groups such as the Mathieu groups, homology of crystallographic groups, homology of nilpotent groups, homology ...
openaire +1 more source
AbstractThis chapter introduces the basic ingredients of the cohomology of groups and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: integral homology of finite groups such as the Mathieu groups, homology of crystallographic groups, homology of nilpotent groups, homology ...
openaire +1 more source
The Cohomology of Extraspecial Groups
Bulletin of the London Mathematical Society, 1992This article is devoted to the cohomology of extraspecial \(p\)-groups. The authors point out the following purposes of the article: to provide a coherent and simplified account of much of the work which has been done in this area; to explain the current state of knowledge; to demonstrate a few of the many techniques which can be used in the field ...
Benson, D. J., Carlson, Jon F.
openaire +2 more sources
Cohomology of groups and transfer
The Annals of Mathematics, 1953The purpose of this paper is to show how the transfer (Verlagerung) of a group A into a subgroup B of finite index can be obtained and generalized in the framework of the cohomology theory of groups (cf. [3]1) and of abstract complexes over a ring [2]. The generalized transfers are homomorphisms of the cohomology groups of the subgroup B into those of ...
openaire +1 more source
Non-Abelian Cohomology of Groups
gmj, 1997Abstract Following Guin's approach to non-abelian cohomology [Guin, Pure Appl. Algebra 50: 109–137, 1988] and, using the notion of a crossed bimodule, a second pointed set of cohomology is defined with coefficients in a crossed module, and Guin's six-term exact cohomology sequence is extended to a nine-term exact sequence of cohomology ...
openaire +2 more sources
On pro-p groups with quadratic cohomology
Journal of Algebra, 2022Claudio Quadrelli, Matteo Vannacci
exaly
On the Integral Cohomology of Bianchi Groups
Experimental Mathematics, 2011Mehmet Haluk Sengun
exaly