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Squares in the Centre of the Group Algebra of a Symmetric Group
Author(s) -
Murray John
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609301008591
Subject(s) - mathematics , subalgebra , group (periodic table) , image (mathematics) , group algebra , combinatorics , field (mathematics) , element (criminal law) , exponent , algebra over a field , pure mathematics , linguistics , chemistry , philosophy , organic chemistry , artificial intelligence , computer science , political science , law
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 → z p , for z ∈ Z , lies in span Z p ′ of the p ‐regular class sums. When p = 2, the image even coincides with Z 2′ . Furthermore, in all cases Z p ′ forms a subalgebra of Z . Let p t be the p ‐exponent of S( n ). Thenj p t= 0 , for each element j of the Jacobson radical J of Z . It is shown that there exists j ∈ J such thatj p t − 1≠ 0 . Most of the results are formulated in terms of the p ‐blocks of S( n ).