极大子群的正特征类和共轭类的表示增长
Representation Growth in positive characteristic and conjugacy classes of maximal subgroups
摘要：
研究了李型有限群的正特征交替群和对称群的表示增长和限制表示增长。我们证明了维数至多为n的表示的个数由n中的一个低次多项式限定。结果证明了有限几乎单群G的极大子群的共轭类个数至多为O（log |G|）.
英文摘要：
We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show that the the number of representations of dimension at most n is bounded by a low degree polynomial in n. As a consequence, we show that the number of conjugacy classes of maximal subgroups of a finite almost simple group G is at most O(log|G|).
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