On the permutation modules for orthogonal groups $O_{m}^{\pm}(3)$ acting on nonsingular points of their standard modules

Details On the permutation modules for orthogonal groups $O_{m}^{\pm}(3)$ acting on nonsingular points of their standard modules On the permutation modules for orthogonal groups $O_{m}^{\pm}(3)$ acting on nonsingular points of their standard modules

2010-01-14

arxiv.org/abs/1001.2346v2

Mathematics

Group Theory

19 pages, 3 tables

Scientific paper

We describe the structure, including composition factors and submodule lattices, of cross-characteristic permutation modules for the natural actions of the orthogonal groups $O_{m}^{\pm}(3)$ with $m\geq6$ on nonsingular points of their standard modules. These actions together with those studied in \cite{HN} are all examples of primitive rank 3 actions of finite classical groups on nonsingular points.

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