Squares in the centre of the group algebra of a symmetric group
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
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).
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