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Murray, John (2002) Squares in the centre of the group algebra of a symmetric group. Bulletin of the London Mathematical Society, 34. pp. 155-164. ISSN 1469-2120
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Abstract
Let Z be the centre of the group algebra of a symmetric group S(n) over a field F characteristic p. One of the principal results of this paper is that the image of the Frobenius map z → zp, for z ∈ Z, lies in span Zp′ of the p-regular class sums. When p = 2, the image even coincides with Z2′. Furthermore, in all cases Zp′ forms a subalgebra of Z. Let pt be the p-exponent of S(n). Then , for each element j of the Jacobson radical J of Z. It is shown that there exists j ∈ J such that . Most of the results are formulated in terms of the p-blocks of S(n).
| Item Type: | Article |
|---|---|
| Keywords: | Group algebra of a symmetric group; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 2155 |
| Depositing User: | Dr. John Murray |
| Date Deposited: | 07 Oct 2010 11:52 |
| Journal or Publication Title: | Bulletin of the London Mathematical Society |
| Publisher: | Oxford University Press, |
| Refereed: | Yes |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/2155 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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