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Squares in the Centre of the Group Algebra of a Symmetric Group

Squares in the Centre of the Group Algebra of a Symmetric Group 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 jpt=0, for each element j of the Jacobson radical J of Z. It is shown that there exists j ∈ J such that jpt−1≠0. Most of the results are formulated in terms of the p‐blocks of S(n). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Squares in the Centre of the Group Algebra of a Symmetric Group

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References (6)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609301008591
Publisher site
See Article on Publisher Site

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 jpt=0, for each element j of the Jacobson radical J of Z. It is shown that there exists j ∈ J such that jpt−1≠0. Most of the results are formulated in terms of the p‐blocks of S(n).

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Mar 1, 2002

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