Hyperbolic modules and cyclic subgroups

Details Hyperbolic modules and cyclic subgroups Hyperbolic modules and cyclic subgroups

2004-12-19

arxiv.org/abs/math/0412384v1

Mathematics

Group Theory

Scientific paper

Let $G$ be a finite group of odd order, $\F$ a finite field of odd
characteristic $p$ and $\B$ a finite--dimensional symplectic $\F G$-module. We
show that $\B$ is $\F G$-hyperbolic, i.e., it contains a self--perpendicular
$\F G$-submodule, iff it is $\F N$-hyperbolic for every cyclic subgroup $N$ of
$G$.

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