Primitive central idempotents of finite group rings of symmetric and alternating groups in characteristic 2
نویسنده
چکیده
and call it the essential weight of the partition μ. For our purpose it is convenient to ignore the parts equal to 1 in the partition because an element like (1, 2, 3) ∈ S3 is also an element of bigger symmetric groups. So we write μ = 22 , ..., nn for a partition and the corresponding class Cμ is a class of an arbitrary symmetric group Sn with n ≥ W (μ) depending on the context, i.e. C2 denotes the conjugacy class of transpositions in every symmetric group Sn, n ≥ 2. If μ = 22 , ..., nn is a partition we write 2α2 , ..., nαn for the class sum C μ ∈ F2Sm, where m ≥W (μ). According to Theorem 1 of [1] one can easily deduce the primitive central idempotents of F2Sn for n < 54 from the primitive central idempotents of F2S54 and F2S53. To simplify that task we added tokens of the form |16 to indicate where the primitive central idempotent of F2S16 ends.
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Primitive central idempotents of finite group rings of symmetric groups
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