李型秩1群及相关群的具有少量若尔当块的模
Modules with few Jordan blocks for rank $1$ groups of Lie type and related groups
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中文总结 AI 辅助
本文针对具有强p嵌入子群的有限群X，研究其k-活跃忠实FF_pX模的非平凡合成因子，其中k不超过X的p-秩m（m≥2）。
中文摘要 AI 辅助
设p为素数，X为具有强p嵌入子群的有限群，例如特征p下的李型秩1群，记m为X的p-秩且假设m≥2。我们称一个忠实的FF_pX模为k-活跃的，若X中某个p阶元素恰有k个非平凡若尔当块。本文确定了对某个k≤m为k-活跃的忠实FF_pX模的非平凡合成因子。
英文摘要
Suppose that $p$ is a prime and $X$ is a finite group with a strongly $p$-embedded subgroup, for example a rank $1$ group of Lie type in characteristic $p$. Let $m$ denote the $p$-rank of $X$ and assume that $m \ge 2$. We say that a faithful $\FF_p X$-module is $k$-active if some element of order $p$ in $X$ acts with exactly $k$ non-trivial Jordan blocks. In this paper, we determine the non-trivial composition factors of the faithful $\FF_pX$-modules which are $k$-active for some $k\leq m$.
