Character Theory of Finite Groups
Character Theory of Finite Groups
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DOI：
10.1090/conm/524
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
M. Lewis;G. Navarro;D. Passman;T. Wolf
中科院分区：
文献类型：
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作者：
M. Lewis;G. Navarro;D. Passman;T. Wolf
1.(I)设K是An中包含的一个共轭类，则K称为分裂的，如果K是An的两个共轭类的并。证明了An中包含的分裂共轭类的个数等于χ∈irr(Sn)的特征标数，使得χAn不是不可约的。(提示。考虑A上的类函数的向量空间，它们在转置(12)的共轭下是不变的。
1. (i) Suppose K is a conjugacy class of Sn contained in An; then K is called split if K is a union of two conjugacy classes of An. Show that the number of split conjugacy classes contained in An is equal to the number of characters χ ∈ Irr(Sn) such that χAn is not irreducible. (Hint. Consider the vector space of class functions on An which are invariant under conjugation by the transposition (12).)