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SQUARES IN THE CENTRE OF THE GROUP ALGEBRA OF A SYMMETRIC GROUP
Published online by Cambridge University Press: 15 March 2002
Abstract
Let Z be the centre of the group algebra of a symmetric group [Sscr ](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 [Sscr ](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 [Sscr ](n).
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- © 2002 The London Mathematical Society
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