关于三角群的有限单象
On finite simple images of triangle groups
摘要：
对于特征为p的单代数群G，如果G的除a，b，c的阶元的子簇的维数和为2dim G，则称一个正整数三元组（a，b，c）对G是刚性的.本文证明了第三作者的一个猜想，即对于p>0的G的刚性三元组（a，b，c），三角群T_{a,b,c}只有1/2个G（p^r）形式的简单象.我们还得到了关于猜想的更一般形式的进一步结果，其中象G（p^r）可以是G型的任意拟单群.
英文摘要：
For a simple algebraic group G in characteristic p, a triple (a,b,c) of positive integers is said to be rigid for G if the dimensions of the subvarieties of G of elements of order dividing a,b,c sum to 2dim G. In this paper we complete the proof of a conjecture of the third author, that for a rigid triple (a,b,c) for G with p>0, the triangle group T_{a,b,c} has only finitely many simple images of the form G(p^r). We also obtain further results on the more general form of the conjecture, where the images G(p^r) can be arbitrary quasisimple groups of type G.
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