The Symmetry of the Modular Burnside Ring
✍ Scribed by Markus Deiml
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 91 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Let b G be the Burnside ring of a finite group G and let k be a field of prime characteristic. It is the purpose of this paper to give a characterization of whether a Ž . block of k m b G is a symmetric k-algebra. This proves a blockwise version of a ޚ Ž . Ž corresponding result about k m b G by W. Gustafson 1977, Comm. Algebra 5, ޚ . 1᎐15 .
📜 SIMILAR VOLUMES
Let G be a finite group and S a finite G-monoid. A crossed G-set over S is a finite G-set equipped with a G-map into S called a weight function. A crossed Ž . Burnside ring X ⍀ G, S is the Grothendieck ring of the category of crossed G-sets with respect to disjoint unions and tensor products. In thi
We determine the number of blocks of the generalized Burnside ring of the symmetric group S with respect to the Young subgroups of S over a field of n n characteristic p. Let kS be a group algebra of S over a field k of characteristic n n Ž . p ) 0 and R R kS the Grothendieck ring of kS over p-local
If V is a faithful module for a finite group G over a field of characteristic p, then the ring of invariants need not be Cohen᎐Macaulay if p divides the order of G. In this article the cohomology of G is used to study the question of Cohen᎐Macaulayness of the invariant ring. One of the results is a