The cohomology rings of certain finite permutation representations-Reference-Cited by-同舟云学术

The cohomology rings of certain finite permutation representations

Published:1974 Issue:2 Volume:45 Page:157-163
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Blowers James V.

Abstract

In this paper the concept of join of two permutation representations is defined and the cohomology of this join is computed and shown to have trivial cup-products. This computation is then used to compute the cohomology groups of the p p -Sylow subgroup of a symmetric group of order n n acting on the set of n n elements, and it is shown that the ring structure on these groups is not finitely generated, although it is transitive.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-045-02/S0002-9939-1974-0379690-2/S0002-9939-1974-0379690-2.pdf

Reference7 articles.

1. Foundations of relative homological algebra;Eilenberg, Samuel;Mem. Amer. Math. Soc.,1965

2. The cohomology ring of a finite group;Evens, Leonard;Trans. Amer. Math. Soc.,1961

3. A generalization of the transfer map in the cohomology of groups;Evens, Leonard;Trans. Amer. Math. Soc.,1963

4. Generalized group cohomology;Harris, Morton E.;Fund. Math.,1969

5. Homology of the infinite symmetric group;Nakaoka, Minoru;Ann. of Math. (2),1961

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The relative Heller operator and relative cohomology for the Klein 4-group;Communications in Algebra;2021-10-16

2. Comparison of relative group (co)homologies;Boletín de la Sociedad Matemática Mexicana;2016-09-14

3. On the cohomology rings of small categories;Journal of Pure and Applied Algebra;2008-11

4. Relative cohomology of finite groups and polynomial growth;Journal of Pure and Applied Algebra;1994-11

5. Complexity and multiple complexes;Mathematische Zeitschrift;1987-06