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Hyperbolic modules and cyclic subgroups

Maria Loukaki
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Abstract

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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Maria Loukaki. 2004-12-19. Hyperbolic modules and cyclic subgroups. https://arxiv.org/abs/math/0412384

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